Critical regularity of nonlinearities in semilinear effectively damped wave models

AIMS Mathematics

article

Abdelhamid Mohammed Djaouti¹  Michael Reissig² 

[1] Preparatory Year Deanship, King Faisal University;Faculty for Mathematics and Computer Science, Technical University Bergakademie

关键词: damped wave equations;    time dependent dissipation;    global existence;    blow-up;    critical regularity;   

DOI  :  10.3934/math.2023236

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper we consider the Cauchy problem for the semilinear effectively damped wave equation$ \begin{equation*} u_{tt}-u_{xx}+b(t)u_{t} = |u|^{3}\mu(|u|), \, \, \, u(0, x) = u_{0}(x), \, \, \, u_{t}(0, x) = u_{1}(x). \end{equation*} $Our goal is to propose sharp conditions on $ \mu $ to obtain a threshold between global (in time) existence of small data Sobolev solutions (stability of the zero solution) and blow-up behaviour even of small data Sobolev solutions.

【 授权许可】

CC BY