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Local Well-Posedness of the Cauchy Problem for a \(p\)-Adic Nagumo-Type Equation

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Abstract

We introduce a new family of \(p\)-adic nonlinear evolution equations. We establish the local well-posedness of the Cauchy problem for these equations in Sobolev-type spaces. For a certain subfamily, we show that the blow-up phenomenon occurs and provide numerical simulations showing this phenomenon.

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Funding

The third author was partially supported by the Lokenath Debnath Endowed Professorship, UTRGV.

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Authors and Affiliations

  1. Pontificia Universidad Javeriana, Departamento de Matemáticas, Cra. 7 N. 40-62, Bogotá D.C., Colombia

    L. F. Chacón-Cortés

  2. Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Departamento de Matemáticas, Unidad Querétaro, Libramiento Norponiente #2000, Fracc. Real de Juriquilla, Santiago de Querétaro, Qro. 76230, México

    C. A. Garcia-Bibiano

  3. University of Texas Rio Grande Valley, School of Mathematical & Statistical Sciences, One West University Blvd., Brownsville, TX 78520, United States

    W. A. Zúñiga-Galindo

Authors
  1. L. F. Chacón-Cortés
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  2. C. A. Garcia-Bibiano
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  3. W. A. Zúñiga-Galindo
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Corresponding authors

Correspondence to L. F. Chacón-Cortés, C. A. Garcia-Bibiano or W. A. Zúñiga-Galindo.

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Chacón-Cortés, L.F., Garcia-Bibiano, C.A. & Zúñiga-Galindo, W.A. Local Well-Posedness of the Cauchy Problem for a \(p\)-Adic Nagumo-Type Equation. P-Adic Num Ultrametr Anal Appl 14, 279–296 (2022). https://doi.org/10.1134/S2070046622040021

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  • DOI: https://doi.org/10.1134/S2070046622040021

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