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arXiv · 1904.02939

Critical regularity of nonlinearities in semilinear classical damped wave equations

Marcelo Rempel Ebert·Giovanni Girardi·Michael Reissig
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Abstract

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

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Marcelo Rempel Ebert, Giovanni Girardi, Michael Reissig. 2019-04-05. Critical regularity of nonlinearities in semilinear classical damped wave equations. https://arxiv.org/abs/1904.02939

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