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.
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页码：2501 / 2532
页数：32
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