Critical regularity of nonlinearities in semilinear classical damped\n wave equations

2019/04/05 by Marcelo Rempel Ebert, Ebert, Marcelo Rempel, Giovanni Girardi +3 · 3 citations
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.1904.02939

openalex publication_date 2019/04/05 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the Cauchy problem for the semilinear damped wave\nequation\n u_tt-\Δ u + u_t = h(u); u(0;x) = f(x); u_t(0;x) = g(x);\n where h(s) = |s|^1+2/n\μ(|s|). Here n is the space dimension and \μ\nis a modulus of continuity. Our goal is to obtain sharp conditions on \μ to\nobtain a threshold between global (in time) existence of small data solutions\n(stability of the zerosolution) and blow-up behavior even of small data\nsolutions.\n

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