Finite Time Blow-Up for Wave Equations with Strong Damping in an Exterior Domain

被引：9

作者：

Fino, Ahmad Z. ^{[1
]}

机构：

[1] Lebanese Univ, Fac Sci, Dept Math, POB 1352, Tripoli, Lebanon

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2020年 / 17卷 / 06期

关键词：

Semilinear wave equation; blow-up; exterior domain; strong damping; CRITICAL EXPONENT; WEAK SOLUTIONS; EXISTENCE;

D O I：

10.1007/s00009-020-01607-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the initial boundary value problem in exterior domain for strongly damped wave equations with power-type nonlinearity vertical bar u vertical bar(p). We will establish blow-up results under some conditions on the initial data and the exponentp, using the method of test function with an appropriate harmonic functions. We also study the existence of mild solution and its relation with the weak formulation.

引用

页数：21

共 50 条

[41] Blow-up of solutions for coupled wave equations with damping terms and derivative nonlinearities
Ming, Sen
Wang, Xiaodong
Fan, Xiongmei
Wu, Xiao
AIMS MATHEMATICS, 2024, 9 (10): : 26854 - 26876
[42] A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations
Chien-Hong Cho
NumericalMathematics:Theory,MethodsandApplications, 2010, (04) : 475 - 498
[43] Blow-up of solutions for nonlinear wave equations on locally finite graphs
Hong, Desheng
AIMS MATHEMATICS, 2023, 8 (08): : 18163 - 18173
[44] Blow-Up Results for Viscoelastic Wave Equations with Damping Terms on Stratified Groups
Kassymov, Aidyn
Kashkynbayev, Ardak
Suragan, Durvudkhan
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2022, 45 (05) : 2549 - 2570
[45] A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations
Cho, Chien-Hong
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2010, 3 (04) : 475 - 498
[46] Finite time blow-up for damped wave equations with space–time dependent potential and nonlinear memory
I. Dannawi
M. Kirane
A. Z. Fino
Nonlinear Differential Equations and Applications NoDEA, 2018, 25
[47] FINITE-TIME BLOW-UP FOR SOLUTIONS OF NON-LINEAR WAVE-EQUATIONS
GLASSEY, RT
MATHEMATISCHE ZEITSCHRIFT, 1981, 177 (03) : 323 - 340
[48] Uniqueness of boundary blow-up solutions on exterior domain of RN
Dong, Wei
Pang, Changci
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 330 (01) : 654 - 664
[49] General decay and blow-up of solutions for a nonlinear viscoelastic wave equation with strong damping
Qian Li
Luofei He
Boundary Value Problems, 2018
[50] General decay and blow-up of solutions for a nonlinear viscoelastic wave equation with strong damping
Li, Qian
He, Luofei
BOUNDARY VALUE PROBLEMS, 2018,

← 1 2 3 4 5 →