Mathematical analysis of memory effects and thermal relaxation in\n nonlinear sound waves on unbounded domains

2020/03/26 by Vanja Nikolić, Nikolić, Vanja, Belkacem Said‐Houari +1
Computer Science · Engineering · Mathematics · #35G25 #35L75 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2003.11840

openalex publication_date 2020/03/26 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Motivated by the propagation of nonlinear sound waves through relaxing\nhereditary media, we study a nonlocal third-order Jordan-Moore-Gibson-Thompson\nacoustic wave equation. Under the assumption that the relaxation kernel decays\nexponentially, we prove local well-posedness in unbounded two- and\nthree-dimensional domains. In addition, we show that the solution of the\nthree-dimensional model exists globally in time for small and smooth data,\nwhile the energy of the system decays polynomially.\n

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