Critical regularity of nonlinearities in semilinear classical damped wave equations
| Autor: | Ebert, Marcelo Rempel, Girardi, Giovanni, Reissig, Michael |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we consider the Cauchy problem for the semilinear damped wave equation $u_{tt}-\Delta u + u_t = h(u);\qquad u(0;x) = f(x); \quad u_t(0;x) = g(x);$ where $h(s) = |s|^{1+2/n}\mu(|s|)$. Here n is the space dimension and $\mu$ is a modulus of continuity. Our goal is to obtain sharp conditions on $\mu$ 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. Comment: 14 pages |
| Databáze: | arXiv |
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