Well-posedness and global extensibility criteria for time-fractionally damped Jordan--Moore--Gibson--Thompson equation

2024/10/23 by Mostafa Meliani, Meliani, Mostafa, Belkacem Said‐Houari +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2410.17826

openalex publication_date 2024/10/23 · openalex created_date 2024/11/13 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the Jordan--Moore--Gibson--Thompson with a time-fractional damping term of the type δ\textupD_t^1-α Δ\psit where we allow the challenging so-called critical case (δ=0). This equation arises in the context of acoustic propagation through thermally relaxed media. We tackle the question of long-time existence of the solution. More precisely, the goal of the paper is twofold: First, we establish local well-posedness of the initial boundary value problem, where we also provide a lower bound on the final time of existence as a function of initial data. Second, we prove a regularity result which guarantees, under the hypothesis of boundedness of certain quantities, that the local solution can be extended to be global-in-time.

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• Global existence for a fractionally damped nonlinear Jordan--Moore--Gibson--Thompson equation

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