Finite time blow-up for damped wave equations with space-time dependent potential and nonlinear memory

被引：11

作者：

Dannawi, I. ^{[1
]}

Kirane, M. ^{[2
,3
,4
]}

Fino, A. Z. ^{[5
]}

机构：

[1] Lebanese Int Univ, Dept Math, Fac Sci, Tripoli, Lebanon

[2] King Abdulaziz Univ, NAAM Res Grp, Dept Math, Fac Sci, POB 80203, Jeddah 21589, Saudi Arabia

[3] Univ La Rochelle, LaSIE, Pole Sci & Technol, Ave Michel Crepeau, F-17031 La Rochelle, France

[4] RUDN Univ, 6 Miklukho Maklay St, Moscow 117198, Russia

[5] Lebanese Univ, Dept Math, Fac Sci 3, Tripoli, Lebanon

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2018年 / 25卷 / 05期

关键词：

Nonlinear damped wave equation; Local existence; Blow-up; Subcritical potential; CRITICAL EXPONENT; GLOBAL EXISTENCE; STABILITY;

D O I：

10.1007/s00030-018-0533-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the Cauchy problem in R-N, n >= 1, for semilinear damped wave equations with space-time dependent potential and nonlinear memory. A blow-up result under some positive data in any dimensional space is obtained. Moreover, the local existence in the energy space is also studied.

引用

页数：19

共 27 条

[1]

CAZENAVE T, 1990, INTRO PROBLEMES EVOL

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

D'Abbicco, M. .

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

[3] A wave equation with structural damping and nonlinear memory [J].

D'Abbicco, Marcello .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2014, 21 (05) :751-773

[4]

Debnath L, 2007, Integral Transforms and Their Applications, DOI DOI 10.1201/9781420010916

[5]

Fino A.Z, FINITE TIME BL UNPUB

[6] Decay of mass for nonlinear equation with fractional Laplacian [J].

Fino, Ahmad ;

Karch, Grzegorz .

MONATSHEFTE FUR MATHEMATIK, 2010, 160 (04) :375-384

[7] QUALITATIVE PROPERTIES OF SOLUTIONS TO A TIME-SPACE FRACTIONAL EVOLUTION EQUATION [J].

Fino, Ahmad Z. ;

Kirane, Mokhtar .

QUARTERLY OF APPLIED MATHEMATICS, 2012, 70 (01) :133-157

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

Fino, Ahmad Z. .

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

[9]

FUJITA H, 1966, J FAC SCI U TOKYO 1, V13, P109

[10] EXISTENCE OF A SOLUTION OF THE WAVE-EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS [J].

GEORGIEV, V ;

TODOROVA, G .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 109 (02) :295-308

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