In this paper we consider the Cauchy problem for the semilinear damped wave equation utt-Δu+ut=h(u),u(0,x)=ϕ(x),ut(0,x)=ψ(x),where h(s)=|s|1+2nμ(|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 zero solution) and blow-up behavior even of small data solutions
Critical regularity of nonlinearities in semilinear classical damped wave equations / Ebert, Mr; Girardi, G; Reissig, M. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 378:3-4(2020), pp. 1311-1326. [10.1007/s00208-019-01921-5]
Critical regularity of nonlinearities in semilinear classical damped wave equations
Girardi, G;
2020-01-01
Abstract
In this paper we consider the Cauchy problem for the semilinear damped wave equation utt-Δu+ut=h(u),u(0,x)=ϕ(x),ut(0,x)=ψ(x),where h(s)=|s|1+2nμ(|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 zero solution) and blow-up behavior even of small data solutions| File | Dimensione | Formato | |
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