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
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 solutionsFile in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
