A COMPETITION ON BLOW-UP FOR SEMILINEAR WAVE EQUATIONS WITH SCALE-INVARIANT DAMPING AND NONLINEAR MEMORY TERM

被引：3

作者：

Chen, Wenhui ^{[1
]}

Fino, Ahmad Z. ^{[2
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Peoples R China

[2] Amer Univ Middle East, Coll Engn & Technol, Dept Math, Kuwait, Kuwait

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2023年 / 16卷 / 06期

关键词：

Semilinear wave equation; scale-invariant damping; power nonlinearity; nonlinear memory; Riemann-Liouville fractional integral; blow-up; LIFE-SPAN; STRAUSS EXPONENT; EXISTENCE; MODELS;

D O I：

10.3934/dcdss.2022169

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate blow-up of solutions to semilinear wave equations with scale-invariant damping and nonlinear memory term in Rn, which can be represented by the Riemann-Liouville fractional integral of order 1- gamma with gamma is an element of (0, 1). Our main interest is to study mixed influence from damping term and the memory kernel on blow-up conditions for the power of nonlinearity, by using test function method or generalized Kato's type lemma. We find a new competition, particularly for the small value of gamma, on the blow-up range between the effective case and the non-effective case.

引用

页码：1264 / 1285

页数：22

共 34 条

[1] A NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF NON NEGATIVE SOLUTIONS FOR SOME SEMILINEAR NON MONOTONE EQUATIONS [J].

BARAS, P ;

PIERRE, M .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1985, 2 (03) :185-212

[2] Existence and blow-up of solutions for damped wave system with nonlinear memory [J].

Berbiche, Mohamed .

APPLICABLE ANALYSIS, 2015, 94 (12) :2535-2564

[3] Interplay effects on blow-up of weakly coupled systems for semilinear wave equations with general nonlinear memory terms [J].

Chen, Wenhui .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2021, 202

[4] The influence of a nonlinear memory on the damped wave equation [J].

D'Abbicco, M. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 95 :130-145

[5] A shift in the Strauss exponent for semilinear wave equations with a not effective damping [J].

D'Abbicco, Marcello ;

Lucente, Sandra ;

Reissig, Michael .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (10) :5040-5073

[6] The threshold of effective damping for semilinear wave equations [J].

D'Abbicco, Marcello .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (06) :1032-1045

[7]

DAbbicco M., 2015, Discrete Contin. Dyn. Syst, P312, DOI [10.3934/proc.2015.0312, DOI 10.3934/PROC.2015.0312]

[8] Finite time blow-up for damped wave equations with space-time dependent potential and nonlinear memory [J].

Dannawi, I. ;

Kirane, M. ;

Fino, A. Z. .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2018, 25 (05)

[9]

Erdelyi A., 1953, Higher Transcendental Functions, VI

[10] Critical exponent for damped wave equations with nonlinear memory [J].

Fino, Ahmad Z. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (16) :5495-5505

← 1 2 3 4 →