In this paperweconsider theCauchy problem for the semilinear dampedwave equationutt -.u + ut = h(u), u(0, x) = f(x), ut (0, x) =.(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 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 paperweconsider theCauchy problem for the semilinear dampedwave equationutt -.u + ut = h(u), u(0, x) = f(x), ut (0, x) =.(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 zero solution) and blow-up behavior even of small data solutions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
