SMALL PERTURBATION OF A SEMILINEAR PSEUDO-PARABOLIC EQUATION

被引：13

作者：

Cao, Yang ^{[1
]}

Yin, Jingxue ^{[2
]}

机构：

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

[2] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 02期

基金：

高等学校博士学科点专项科研基金;

关键词：

Pseudo-parabolic equation; small perturbation; large time behavior; blow-up; global existence; CRITICAL EXPONENTS; GLOBAL EXISTENCE; BLOW-UP; BEHAVIOR; SYSTEMS; MODEL;

D O I：

10.3934/dcds.2016.36.631

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with large time behavior of solutions for the Cauchy problem of a semilinear pseudo-parabolic equation with small perturbation. It is revealed that small perturbation may develop large variation of solutions with the evolution of time, which is similar to that for the standard heat equation with nonlinear sources.

引用

页码：631 / 642

页数：12

共 20 条

[1]

Alshin A. B., 2011, DE GRUYTER SERIES NO, V15

[2] Critical exponents of fujita type for inhomogeneous parabolic equations and systems [J].

Bandle, C ;

Levine, HA ;

Zhang, QS .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 251 (02) :624-648

[3] MODEL EQUATIONS FOR LONG WAVES IN NONLINEAR DISPERSIVE SYSTEMS [J].

BENJAMIN, TB ;

BONA, JL ;

MAHONY, JJ .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1972, 272 (1220) :47-+

[4] Cauchy problems of semilinear pseudo-parabolic equations [J].

Cao, Yang ;

Yin, Jingxue ;

Wang, Chunpeng .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (12) :4568-4590

[5] ON A THEORY OF HEAT CONDUCTION INVOLVING 2 TEMPERATURES [J].

CHEN, PJ .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1968, 19 (04) :614-&

[6] Boundary control for a class of pseudo-parabolic differential equations [J].

Hasan, Agus ;

Aamo, Ole Morten ;

Foss, Bjarne .

SYSTEMS & CONTROL LETTERS, 2013, 62 (01) :63-69

[7] The Cauchy problem for an equation of Sobolev type with power non-linearity [J].

Kaikina, EI ;

Naumkin, PI ;

Shishmarev, IA .

IZVESTIYA MATHEMATICS, 2005, 69 (01) :59-111

[8] Small- and waiting-time behavior of a darcy flow model with a dynamic pressure saturation relation [J].

King, J. R. ;

Cuesta, C. M. .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 66 (05) :1482-1511

[9] A global existence result for the equations describing unsaturated flow in porous media with dynamic capillary pressure [J].

Mikelic, Andro .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (06) :1561-1577

[10] Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities [J].

Serrin, J ;

Zou, HH .

ACTA MATHEMATICA, 2002, 189 (01) :79-142

← 1 2 →