Wave equation with p(x, t)-Laplacian and damping term: Blow-up of solutions

被引：64
作者：
Antontsev, Stanislav [1 ]
机构：
[1] Univ Lisbon, CMAF, P-1649003 Lisbon, Portugal
来源：
COMPTES RENDUS MECANIQUE | 2011年 / 339卷 / 12期
关键词：
Waves; Nonlinear wave equation; Energy estimates; Variable nonlinearity; Nonstandard growth conditions; Blow-up; EXISTENCE;
D O I：
10.1016/j.crme.2011.09.001
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
We study the Dirichlet problem for equation U-tt = div(a(x, t)vertical bar del u vertical bar(p(x, t)-2)del u) + alpha Delta u(t) + b(x, t)vertical bar u vertical bar(sigma(x, t)-2)u in which alpha is a nonnegative constant, the coefficients a(x, t), b(x, t) and the exponents of nonlinearity p(x, t), sigma(x, t) are given functions. Under suitable conditions on the data, we study the finite time blow-up of the solutions. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：751 / 755
页数：5
相关论文
共 21 条
[1]   Blow-up of solutions to parabolic equations with nonstandard growth conditions [J].
Antontsev, S. ;
Shmarev, S. .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (09) :2633-2645
[2]   Vanishing solutions of anisotropic parabolic equations with variable nonlinearity [J].
Antontsev, S. ;
Shmarev, S. .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 361 (02) :371-391
[3]  
ANTONTSEV S, 2011, INT C NONL MOD PART
[4]  
ANTONTSEV S, RACSAM REV R ACAD A, P1
[5]  
Antontsev S.N., 2006, Ann. Univ. Ferrara. Sez., VVII, P19, DOI [DOI 10.1007/S11565-006-0002-9, 10.1007/s11565-006-0002-9]
[6]  
Antontsev S. N., 2008, P STEKLOV I MATH, V268, P2289
[7]  
Antontsev S.N., 2002, PROGR NONLINEAR DIFF, V48
[8]  
Antontsev S, 2006, HBK DIFF EQUAT STATI, V3, P1, DOI 10.1016/S1874-5733(06)80005-7
[9]   Decay estimates for the wave equation of p-Laplacian type with dissipation of m-Laplacian type [J].
Benaissa, Abbes ;
Mokeddem, Soufiane .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2007, 30 (02) :237-247
[10]   Blow-up and critical exponents for nonlinear hyperbolic equations [J].
Galaktionov, VA ;
Pohozaev, SI .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 53 (3-4) :453-466
123