SEMILINEAR EVOLUTION MODELS WITH SCALE-INVARIANT FRICTION AND VISCO-ELASTIC DAMPING

被引：0

作者：

Mezadek, Abdelatif Kainane ^{[1
]}

Reissig, Michael ^{[2
]}

机构：

[1] Hassiba Benbouali Univ, Fac Exact Sci & Informat, Lab Math & Applicat, Chlef 021800, Algeria

[2] Tech Univ Bergakademie Freiberg, Inst Appl Anal, Fac Math & Comp Sci, Pruferstr 9, D-09596 Freiberg, Germany

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2023年 / 22卷 / 08期

关键词：

Global in time existence; small data solutions; visco-elastic damping; power non-linearity; higher regularity of data; fractional chain rule; blow-up; critical exponent; WAVE-EQUATIONS;

D O I：

10.3934/cpaa.2023075

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the global (in time) existence of small data Sobolev solutions and blow-up of Sobolev solutions to the Cauchy problem for semilinear evolution models with scale-invariant friction, visco-elastic damping and power nonlinearity. We are interested in critical exponents and the question how higher regularity in the data influences the admissible range of exponents p in the power nonlinearity to get global (in time) small data Sobolev solutions.

引用

页码：2501 / 2532

页数：32

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