In this paper, we propose the compact convergence approach to deal with the continuity of attractors of some reaction–diffusion equations under smooth perturbations of the domain subject to nonlinear Neumann boundary conditions. We define a family of invertible linear operators to compare the dynamics of perturbed and unperturbed problems in the same phase space. All continuity arising from small smooth perturbations will be estimated by a rate of convergence given by the domain variation in a \({\mathcal {C}}^1\) topology.

中文翻译：

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具有非线性诺伊曼边界条件和 $${\mathcal {C}}^1$$ 域变化的反应扩散方程的收敛速度

在本文中，我们提出了紧凑收敛方法来处理非线性诺依曼边界条件下域的平滑扰动下一些反应扩散方程的吸引子连续性。我们定义了一系列可逆线性算子来比较同一相空间中扰动和未扰动问题的动力学。由小的平滑扰动引起的所有连续性将通过由\({\mathcal {C}}^1\)拓扑中的域变化给出的收敛速率来估计。