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Long Run Stochastic Control Problems with General Discounting Appl. Math. Optim. (IF 1.8) Pub Date : 2024-03-26 Łukasz Stettner
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Gevrey Class for Locally Three-Phase-Lag Thermoelastic Beam System Appl. Math. Optim. (IF 1.8) Pub Date : 2024-03-25 Jaime Muñoz Rivera, Elena Ochoa Ochoa, Ramón Quintanilla
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Long and Short Time Behavior of Non-local in Time Subdiffusion Equations Appl. Math. Optim. (IF 1.8) Pub Date : 2024-03-25 Juan C. Pozo, Vicente Vergara
This paper is devoted to studying the long and short time behavior of the solutions to a class of non-local in time subdiffusion equations. To this end, we find sharp estimates of the fundamental solutions in Lebesgue spaces using tools of the theory of Volterra equations. Our results include, as particular cases, the so-called time-fractional and the ultraslow reaction-diffusion equations, which have
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Shape-Programming in Hyperelasticity Through Differential Growth Appl. Math. Optim. (IF 1.8) Pub Date : 2024-03-23 Rogelio Ortigosa-Martínez, Jesús Martínez-Frutos, Carlos Mora-Corral, Pablo Pedregal, Francisco Periago
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Numerical Approximation of the Solution of an Obstacle Problem Modelling the Displacement of Elliptic Membrane Shells via the Penalty Method Appl. Math. Optim. (IF 1.8) Pub Date : 2024-03-05 Aaron Meixner, Paolo Piersanti
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Simultaneous Exact Boundary Controllability of Final State and Nodal Profile for Quasilinear Hyperbolic Systems Appl. Math. Optim. (IF 1.8) Pub Date : 2024-02-26
Abstract In this paper, we consider the problem about the simultaneous realization of exact boundary controllability of final state and nodal profile for general 1-D first order quasilinear hyperbolic systems. We show that by means of boundary controls, the system (hyperbolic equations together with boundary conditions) can drive any given initial data at \(t=0\) to any given final data at \(t=T\)
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Analysis of a Combined Filtered/Phase-Field Approach to Topology Optimization in Elasticity Appl. Math. Optim. (IF 1.8) Pub Date : 2024-02-19 Ferdinando Auricchio, Michele Marino, Idriss Mazari, Ulisse Stefanelli
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Discrete Approximations and Optimality Conditions for Controlled Free-Time Sweeping Processes Appl. Math. Optim. (IF 1.8) Pub Date : 2024-02-16 Giovanni Colombo, Boris S. Mordukhovich, Dao Nguyen, Trang Nguyen
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An Improvement to Prandtl’s 1933 Model for Minimizing Induced Drag Appl. Math. Optim. (IF 1.8) Pub Date : 2024-02-04 Wojciech S. Ożański
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Observability Inequality from Measurable Sets and the Shape Design Problem for Stochastic Parabolic Equations Appl. Math. Optim. (IF 1.8) Pub Date : 2024-01-31 Yuanhang Liu
The primary objective of this paper is to directly establish the observability inequality for stochastic parabolic equations from measurable sets. In an immediate practical application, our focus centers on the investigation of optimal actuator placement to achieve minimum norm controls in the context of approximative controllability for stochastic parabolic equations. We introduce a comprehensive
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Sharp-Interface Limit of a Multi-phase Spectral Shape Optimization Problem for Elastic Structures Appl. Math. Optim. (IF 1.8) Pub Date : 2024-01-09 Harald Garcke, Paul Hüttl, Christian Kahle, Patrik Knopf
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The Cost of Null Controllability for a Backward Stochastic Degenerate Parabolic Equation in the Vanishing Viscosity Limit Appl. Math. Optim. (IF 1.8) Pub Date : 2023-12-19 Qun Chen, Bin Wu
In this paper, we investigate the cost of null controllability for a backward stochastic degenerate parabolic equation with a boundary control in the vanishing viscosity limit. Firstly we obtain a new Carleman estimate for the adjoint stochastic equation. Combining this Carleman estimate and an exponential dissipation estimate, we obtain the uniform null controllability for large control time. When
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Return-to-Normality in a Piecewise Deterministic Markov SIR+V Model with Pharmaceutical and Non-pharmaceutical Interventions Appl. Math. Optim. (IF 1.8) Pub Date : 2023-12-19 Dan Goreac, Juan Li, Yi Wang, Zhengyang Wang
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Robust Feedback Stabilization of Interacting Multi-agent Systems Under Uncertainty Appl. Math. Optim. (IF 1.8) Pub Date : 2023-12-11 Giacomo Albi, Michael Herty, Chiara Segala
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On Optimality of Barrier Dividend Control Under Endogenous Regime Switching with Application to Chapter 11 Bankruptcy Appl. Math. Optim. (IF 1.8) Pub Date : 2023-12-05 Wenyuan Wang, Xiang Yu, Xiaowen Zhou
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Strong Stationarity Conditions for the Optimal Control of a Cahn–Hilliard–Navier–Stokes System Appl. Math. Optim. (IF 1.8) Pub Date : 2023-12-05 Michael Hintermüller, Tobias Keil
This paper is concerned with the distributed optimal control of a time-discrete Cahn–Hilliard–Navier–Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a variational inequality of fourth order and the Navier–Stokes equation. The existence of solutions to the primal system and of optimal controls is established. The Lipschitz
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Dynamics and Stability Analysis for Stochastic 3D Lagrangian-Averaged Navier–Stokes Equations with Infinite Delay on Unbounded Domains Appl. Math. Optim. (IF 1.8) Pub Date : 2023-12-05 Shuang Yang, Tomás Caraballo, Yangrong Li
This paper is devoted to investigating mean dynamics and stability analysis for stochastic 3D Lagrangian-averaged Navier–Stokes (LANS) equations driven by infinite delay on unbounded domains. We first prove the existence of a unique solution to stochastic 3D LANS equations with infinite delay when the non-delayed external force is locally integrable, the delay term is globally Lipschitz continuous
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Boundedness Through Nonlocal Dampening Effects in a Fully Parabolic Chemotaxis Model with Sub and Superquadratic Growth Appl. Math. Optim. (IF 1.8) Pub Date : 2023-11-28 Yutaro Chiyo, Fatma Gamze Düzgün, Silvia Frassu, Giuseppe Viglialoro
This work deals with a chemotaxis model where an external source involving a sub and superquadratic growth effect contrasted by nonlocal dampening reaction influences the motion of a cell density attracted by a chemical signal. We study the mechanism of the two densities once their initial configurations are fixed in bounded impenetrable regions; in the specific, we establish that no gathering effect
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Continuity Properties of Pullback and Pullback Exponential Attractors for Non-autonomous Plate with $$p-$$ Laplacian Appl. Math. Optim. (IF 1.8) Pub Date : 2023-11-30 Moncef Aouadi
Our purpose is to study some continuity properties of pullback and pullback exponential attractors for the non-autonomous plate with \(p-\)Laplacian and nonlocal weak damping \(\text {g}_\epsilon (\Vert u_t\Vert )u_t\) under hinged boundary condition. Moreover, the existence of pullback attractors in the natural space energy with finite dimensionality is proved together with its upper semicontinuity
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Optimal Distributed Control for a Viscous Non-local Tumour Growth Model Appl. Math. Optim. (IF 1.8) Pub Date : 2023-11-27 Matteo Fornoni
In this paper, we address an optimal distributed control problem for a non-local model of phase-field type, describing the evolution of tumour cells in presence of a nutrient. The model couples a non-local and viscous Cahn–Hilliard equation for the phase parameter with a reaction-diffusion equation for the nutrient. The optimal control problem aims at finding a therapy, encoded as a source term in
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Importance Sampling for the Empirical Measure of Weakly Interacting Diffusions Appl. Math. Optim. (IF 1.8) Pub Date : 2023-11-22 Z. W. Bezemek, M. Heldman
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Stackelberg Game Approach to Mixed Stochastic $$H_{2}/H_{\infty }$$ Control for Mean-Field Jump-Diffusions Systems Appl. Math. Optim. (IF 1.8) Pub Date : 2023-11-18 Suya Zhang, Weihai Zhang, Qingxin Meng
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Global Well-Posedness, Mean Attractors and Invariant Measures of Generalized Reversible Gray–Scott Lattice Systems Driven by Nonlinear Noise Appl. Math. Optim. (IF 1.8) Pub Date : 2023-11-14 Xiaolan Qin, Renhai Wang
The main objective of our investigation is to study the global well-posedness as well as stochastic dynamics of a class of generalized reversible Gray–Scott lattice systems (RGSLSs) driven by nonlinear white noise. Compared with the classical stochastic RGSLSs considered in the literature, the generalized stochastic RGSLSs have two significant features: the coupled drift terms have polynomial growth
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Linear-Quadratic Delayed Mean-Field Social Optimization Appl. Math. Optim. (IF 1.8) Pub Date : 2023-11-09 Tianyang Nie, Shujun Wang, Zhen Wu
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Approximate Optimal Control of Fractional Impulsive Partial Stochastic Differential Inclusions Driven by Rosenblatt Process Appl. Math. Optim. (IF 1.8) Pub Date : 2023-11-07 Zuomao Yan
In this paper, we study the approximate optimal control problems for a class of fractional partial stochastic differential inclusions driven by Rosenblatt process and non-instantaneous impulses in a Hilbert space. Firstly, we prove an existence result of mild solutions for the control systems by using stochastic analysis, the fractional calculus, the measure of noncompactness, properties of sectorial
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Numerical Solution to a Free Boundary Problem for the Stokes Equation Using the Coupled Complex Boundary Method in Shape Optimization Setting Appl. Math. Optim. (IF 1.8) Pub Date : 2023-11-07 Julius Fergy Tiongson Rabago, Hirofumi Notsu
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Fast Continuous Dynamics Inside the Graph of Subdifferentials of Nonsmooth Convex Functions Appl. Math. Optim. (IF 1.8) Pub Date : 2023-11-01 Paul-Emile Maingé, André Weng-Law
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An Extended McKean–Vlasov Dynamic Programming Approach to Robust Equilibrium Controls Under Ambiguous Covariance Matrix Appl. Math. Optim. (IF 1.8) Pub Date : 2023-10-24 Qian Lei, Chi Seng Pun
This paper studies a general class of time-inconsistent stochastic control problems under ambiguous covariance matrix. The time inconsistency is caused in various ways by a general objective functional and thus the associated control problem does not admit Bellman’s principle of optimality. Moreover, we model the state by a McKean–Vlasov dynamics under a set of non-dominated probability measures induced
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Discrete-Time Mean-Field Stochastic Control with Partial Observations Appl. Math. Optim. (IF 1.8) Pub Date : 2023-10-24 Jeremy Chichportich, Idris Kharroubi
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Well-Posedness and Dynamical Properties for Extensible Beams with Nonlocal Frictional Damping and Polynomial Nonlinearity Appl. Math. Optim. (IF 1.8) Pub Date : 2023-10-24 Kailun Chen, Jun Zhou
This paper is concerned with extensible beams with nonlocal frictional damping and polynomial nonlinearity. By using semigroup theory, potential well method, and energy method, the well-posedness and the conditions on global existence and finite time blow-up of solutions are studied. Moreover, the upper bound of blow-up time is also given by using ordinary differential inequalities.
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Generalized Conditional Gradient and Learning in Potential Mean Field Games Appl. Math. Optim. (IF 1.8) Pub Date : 2023-10-24 Pierre Lavigne, Laurent Pfeiffer
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Labor Supply Flexibility and Portfolio Selection with Early Retirement Option Appl. Math. Optim. (IF 1.8) Pub Date : 2023-10-17 Junkee Jeon, Jehan Oh
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Optimal Control of Hughes’ Model for Pedestrian Flow via Local Attraction Appl. Math. Optim. (IF 1.8) Pub Date : 2023-10-17 Roland Herzog, Jan-Frederik Pietschmann, Max Winkler
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Optimal Control of Nonlocal Continuity Equations: Numerical Solution Appl. Math. Optim. (IF 1.8) Pub Date : 2023-10-05 Roman Chertovskih, Nikolay Pogodaev, Maxim Staritsyn
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Riemannian Smoothing Gradient Type Algorithms for Nonsmooth Optimization Problem on Compact Riemannian Submanifold Embedded in Euclidean Space Appl. Math. Optim. (IF 1.8) Pub Date : 2023-10-03 Zheng Peng, Weihe Wu, Jiang Hu, Kangkang Deng
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Strong Stationarity for Optimal Control Problems with Non-smooth Integral Equation Constraints: Application to a Continuous DNN Appl. Math. Optim. (IF 1.8) Pub Date : 2023-09-26 Harbir Antil, Livia Betz, Daniel Wachsmuth
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Fenchel Conjugate via Busemann Function on Hadamard Manifolds Appl. Math. Optim. (IF 1.8) Pub Date : 2023-09-26 Glaydston de C. Bento, João Cruz Neto, Ítalo Dowell L. Melo
In this paper we introduce a Fenchel-type conjugate, given as the supremum of convex functions, via Busemann functions. It is known that Busemann functions are smooth convex functions with constant norm gradient. Our study ensures that our proposal on Fenchel conjugate is the most adequate to cover the absence of approximations by non-constant affine functions on Hadamard manifolds. More precisely
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An Averaging Principle for Fast–Slow-Coupled Neutral Stochastic Differential Equations with Time-Varying Delay Appl. Math. Optim. (IF 1.8) Pub Date : 2023-09-20 Minyu Wu, Wenjie Cao, Fuke Wu
This paper examines the stochastic averaging principle of fast-slow-coupled neutral stochastic differential equations with time-varying delay. Due to the presence of neutral terms, traditional martingale methods and weak convergence techniques are not directly applicable. To overcome these difficulties, this paper gives a more subtle proof for tightness of the slow-varying process. To characterize
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Fast Convergence of Inertial Dynamics with Hessian-Driven Damping Under Geometry Assumptions Appl. Math. Optim. (IF 1.8) Pub Date : 2023-09-20 Jean-François Aujol, Charles Dossal, Van Hao Hoàng, Hippolyte Labarrière, Aude Rondepierre
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Nonlinear BSDEs with Two Optional Doob’s Class Barriers Satisfying Weak Mokobodzki’s Condition and Extended Dynkin Games Appl. Math. Optim. (IF 1.8) Pub Date : 2023-09-20 Tomasz Klimsiak, Maurycy Rzymowski
We study reflected backward stochastic differential equations (RBSDEs) on the probability space equipped with a Brownian motion. The main novelty of the paper lies in the fact that we consider the following weak assumptions on the data: barriers are optional of class (D) satisfying weak Mokobodzki’s condition, generator is continuous and non-increasing with respect to the value-variable (no restrictions
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Mean Field Approximation of an Optimal Control Problem for the Continuity Equation Arising in Smart Charging Appl. Math. Optim. (IF 1.8) Pub Date : 2023-09-15 Adrien Séguret
We consider the optimal control of a finite population of hybrid processes (namely agents state is composed of a discrete and a continuous variable), modeling the optimal charging of a large population of identical plug-in electric vehicles (PEVs). We prove the convergence of the solution and that of the value of a sequence of finite population problems respectively to a solution and the value of a
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Functional Central Limit Theorem and Strong Law of Large Numbers for Stochastic Gradient Langevin Dynamics Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-28 A. Lovas, M. Rásonyi
We study the mixing properties of an important optimization algorithm of machine learning: the stochastic gradient Langevin dynamics (SGLD) with a fixed step size. The data stream is not assumed to be independent hence the SGLD is not a Markov chain, merely a Markov chain in a random environment, which complicates the mathematical treatment considerably. We derive a strong law of large numbers and
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Learning-Informed Parameter Identification in Nonlinear Time-Dependent PDEs Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-23 Christian Aarset, Martin Holler, Tram Thi Ngoc Nguyen
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Superfair Stochastic Games Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-23 János Flesch, Arkadi Predtetchinski, William Sudderth
A two-person zero-sum stochastic game with a nonnegative stage reward function is superfair if the value of the one-shot game at each state is at least as large as the reward function at the given state. The payoff in the game is the limit superior of the expected stage rewards taken over the directed set of all finite stop rules. If the game has countable state and action spaces and if at least one
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Factor- $$\sqrt{2}$$ Acceleration of Accelerated Gradient Methods Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-23 Chanwoo Park, Jisun Park, Ernest K. Ryu
The optimized gradient method (OGM) provides a factor-\(\sqrt{2}\) speedup upon Nesterov’s celebrated accelerated gradient method in the convex (but non-strongly convex) setup. However, this improved acceleration mechanism has not been well understood; prior analyses of OGM relied on a computer-assisted proof methodology, so the proofs were opaque for humans despite being verifiable and correct. In
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On the Optimal Control of a Linear Peridynamics Model Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-17 Tadele Mengesha, Abner J. Salgado, Joshua M. Siktar
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Stochastic 3D Globally Modified Navier–Stokes Equations: Weak Attractors, Invariant Measures and Large Deviations Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-17 Tomás Caraballo, Zhang Chen, Dandan Yang
This paper is mainly concerned with the asymptotic dynamics of non-autonomous stochastic 3D globally modified Navier–Stokes equations driven by nonlinear noise. Based on the well-posedness of such equations, we first show the existence and uniqueness of weak pullback mean random attractors. Then we investigate the existence of (periodic) invariant measures, the zero-noise limit of periodic invariant
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Long-Time Dynamics of the Wave Equation with Nonlocal Weak Damping and Super-Cubic Nonlinearity in 3-D Domains, Part II: Nonautonomous Case Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-17 Senlin Yan, Xiangming Zhu, Chengkui Zhong, Zhijun Tang
In this paper, we study the long-time dynamics for the nonautonomous wave equation with nonlocal weak damping and super-cubic nonlinearity in a bounded smooth domain of \(\mathbb {R}^3.\) Based on the Strichartz estimates for the case of bounded domains, we first prove the global well-posedness of the Shatah–Struwe solutions. Then we establish the the concept of uniform \(\varphi \)-attractor and verify
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Multi–component Cahn–Hilliard Systems with Singular Potentials: Theoretical Results Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-17 C. G. Gal, M. Grasselli, A. Poiatti, J. L. Shomberg
We consider a system of nonlinear diffusion equations modelling (isothermal) phase segregation of an ideal mixture of \(N\ge 2\) components occupying a bounded region \(\Omega \subset \mathbb {R}^{d},\) \(d\le 3\). Our system is subject to a constant mobility matrix of coefficients, a free energy functional given in terms of singular entropy generated potentials and localized capillarity effects. We
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A Zero-Sum Deterministic Impulse Controls Game in Infinite Horizon with a New HJBI-QVI Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-17 Brahim El Asri, Hafid Lalioui, Sehail Mazid
In the present paper, we study a two-player, zero-sum, deterministic differential game with both players adopting impulse controls in infinite-time horizon, under rather weak assumptions on the cost functions. We prove by means of the dynamic programming principle that the lower and upper value functions are continuous and viscosity solutions to the corresponding Hamilton-Jacobi-Bellman-Isaacs (HJBI)
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Non-Markovian Impulse Control Under Nonlinear Expectation Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-17 Magnus Perninge
We consider a general type of non-Markovian impulse control problems under adverse non-linear expectation or, more specifically, the zero-sum game problem where the adversary player decides the probability measure. We show that the upper and lower value functions satisfy a dynamic programming principle (DPP). We first prove the dynamic programming principle (DPP) for a truncated version of the upper
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Optimal Temperature Distribution for a Nonisothermal Cahn–Hilliard System with Source Term Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-16 Pierluigi Colli, Gianni Gilardi, Andrea Signori, Jürgen Sprekels
In this note, we study the optimal control of a nonisothermal phase field system of Cahn–Hilliard type that constitutes an extension of the classical Caginalp model for nonisothermal phase transitions with a conserved order parameter. The system couples a Cahn–Hilliard type equation with source term for the order parameter with the universal balance law of internal energy. In place of the standard
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Constraint Qualification with Schauder Basis for Infinite Programming Problems Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-11 E. M. Bednarczuk, K. W. Leśniewski, K. E. Rutkowski
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Asymptotic Behavior of an Adapted Implicit Discretization of Slowly Damped Second Order Dynamical Systems Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-11 Thierry Horsin, Mohamed Ali Jendoubi
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Non-concave Expected Utility Optimization with Uncertain Time Horizon Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-11 Christian Dehm, Thai Nguyen, Mitja Stadje
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Limiting Behavior of Random Attractors of Stochastic Supercritical Wave Equations Driven by Multiplicative Noise Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-11 Zhang Chen, Bixiang Wang
This paper deals with the limiting behavior of random attractors of stochastic wave equations with supercritical drift driven by linear multiplicative white noise defined on unbounded domains. We first establish the uniform Strichartz estimates of the solutions with respect to noise intensity, and then prove the convergence of the solutions of the stochastic equations with respect to initial data as
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A Simple City Equilibrium Model with an Application to Teleworking Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-11 Yves Achdou, Guillaume Carlier, Quentin Petit, Daniela Tonon
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Reverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-11 David Krejčiřík, Vladimir Lotoreichik, Tuyen Vu
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Stability to Signorini Problem with Pointwise Damping Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-11 Jaime E. Muñoz Rivera, Maria Grazia Naso
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Estimates of Exponential Convergence for Solutions of Stochastic Nonlinear Systems Appl. Math. Optim. (IF 1.8) Pub Date : 2023-08-11 Tomás Caraballo, Faten Ezzine, Mohamed Ali Hammami