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

[1] Global existence of solutions for a weakly coupled system of semilinear damped wave equations
Nishihara, Kenji
Wakasugi, Yuta
JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (08) : 4172 - 4201
[2] ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR A SYSTEM OF SEMILINEAR HEAT EQUATIONS AND THE CORRESPONDING DAMPED WAVE SYSTEM
Nishihara, Kenji
OSAKA JOURNAL OF MATHEMATICS, 2012, 49 (02) : 331 - 348
[3] Global existence and nonexistence of solutions for a system of nonlinear damped wave equations
Takeda, Hiroshi
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 360 (02) : 631 - 650
[4] GLOBAL EXISTENCE OF SOLUTIONS FOR A SYSTEM OF NONLINEAR DAMPED WAVE EQUATIONS
Ogawa, Takayoshi
Takeda, Hiroshi
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2010, 23 (7-8) : 635 - 657
[5] Global existence of solutions for damped wave equations with nonlinear memory
Yang, Han
Shi, Jianli
Zhu, Shihui
APPLICABLE ANALYSIS, 2013, 92 (08) : 1691 - 1703
[6] Large time behavior of solutions for a system of nonlinear damped wave equations
Ogawa, Takayoshi
Takeda, Hiroshi
JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 251 (11) : 3090 - 3113
[7] POINTWISE ESTIMATES FOR SOLUTIONS TO A SYSTEM OF NONLINEAR DAMPED WAVE EQUATIONS
Wang, Wenjun
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013,
[8] Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations in the scattering case with mixed nonlinear terms
Palmieri, Alessandro
Takamura, Hiroyuki
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2020, 27 (06):
[9] Critical exponent for damped wave equations with nonlinear memory
Fino, Ahmad Z.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (16) : 5495 - 5505
[10] GLOBAL SOLUTIONS TO THE CAUCHY PROBLEM FOR A SYSTEM OF DAMPED WAVE EQUATIONS
Narazaki, Takashi
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2011, 24 (5-6) : 569 - 600

← 1 2 3 4 5 →