Global Small data Solutions for a system of semilinear heat equations and the corresponding system of damped wave equations with nonlinear memory

被引：0

作者：

Berbiche, Mohamed ^{[1
]}

Terchi, Messaouda ^{[1
]}

机构：

[1] Univ Biskra, Lab Math Anal Probabil & Optimizat, POB 145, Biskra 07000, Algeria

来源：

ADVANCES IN PURE AND APPLIED MATHEMATICS | 2020年 / 11卷 / 02期

关键词：

Parabolic system; damped wave system; global existence; critical exponent; FUJITA CRITICAL EXPONENT; BLOW-UP; CAUCHY-PROBLEM; R-N; EXISTENCE; ASYMPTOTICS; BEHAVIOR; SPACE;

D O I：

10.21494/ISTE.OP.2020.0555

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Cauchy problem for a strongly coupled semi-linear heat equations with some kind of nonlinearity in multi-dimensional space R-N. We see under some conditions on the exponents and on the dimension N, that the existence and uniqueness of time-global solutions for small data and their asymptotic behaviors are obtained. This observation will be applied to the corresponding system of the damped wave equations in low dimensional space.

引用

页码：57 / 87

页数：31

共 50 条

[21] Global solutions and finite time blow up for damped semilinear wave equations
Gazzola, F
Squassina, M
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2006, 23 (02): : 185 - 207
[22] Global existence and decay of solutions of a nonlinear system of wave equations
Said-Houari, Belkacem
APPLICABLE ANALYSIS, 2012, 91 (03) : 475 - 489
[23] GLOBAL EXISTENCE OF SOLUTIONS FOR HIGHER ORDER NONLINEAR DAMPED WAVE EQUATIONS
Takeda, Hiroshi
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 31 : 1358 - 1367
[24] Global attractor for damped semilinear elastic beam equations with memory
Marzocchi, A
Vuk, E
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2003, 54 (02): : 224 - 234
[25] Global attractor for damped semilinear elastic beam equations with memory
A. Marzocchi
E. Vuk
Zeitschrift für angewandte Mathematik und Physik ZAMP, 2003, 54 : 224 - 234
[26] Global averaging and parametric resonances in damped semilinear wave equations
Zelik, S.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2006, 136 : 1053 - 1097
[27] GLOBAL EXISTENCE FOR SEMILINEAR DAMPED WAVE EQUATIONS IN THE SCATTERING CASE
Bai, Yige
Liu, Mengyun
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2019, 32 (3-4) : 233 - 248
[28] Growth of solutions with positive initial energy to system of degeneratly damped wave equations with memory
Zennir K.
Lobachevskii Journal of Mathematics, 2014, 35 (2) : 147 - 156
[29] On the existence of global solutions of a system of semilinear parabolic equations with nonlinear nonlocal boundary conditions
A. L. Gladkov
A. I. Nikitin
Differential Equations, 2016, 52 : 467 - 482
[30] On the existence of global solutions of a system of semilinear parabolic equations with nonlinear nonlocal boundary conditions
Gladkov, A. L.
Nikitin, A. I.
DIFFERENTIAL EQUATIONS, 2016, 52 (04) : 467 - 482

← 1 2 3 4 5 →