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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Critical regularity of nonlinearities in semilinear classical damped wave equations

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Author(s):
Ebert, M. R. [1] ; Girardi, G. [2] ; Reissig, M. [3]
Total Authors: 3
Affiliation:
[1] Univ Sao Paulo, Dept Comp & Matemat, FFCLRP, Av Bandeirantes 3900, BR-14040901 Ribeirao Preto, SP - Brazil
[2] Univ Bari Aldo Moro, Dipartimento Matemat, Via Orabona 4, Bari - Italy
[3] Tech Univ Bergakad Freiberg, Fac Math & Comp Sci, Pruferstr 9, D-09596 Freiberg - Germany
Total Affiliations: 3
Document type: Journal article
Source: MATHEMATISCHE ANNALEN; OCT 2019.
Web of Science Citations: 0
Abstract

In this paperweconsider theCauchy problem for the semilinear dampedwave equation utt -.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. (AU)

FAPESP's process: 18/10231-3 - A classification for wave models with time-dependent mass and integrable speed of propagation
Grantee:Marcelo Rempel Ebert
Support type: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 17/19497-3 - Asymptotic profile of solutions for some evolution partial differential equations and applications
Grantee:Marcelo Rempel Ebert
Support type: Regular Research Grants