INITIAL BOUNDARY VALUE PROBLEM OF A CLASS OF MIXED PSEUDO-PARABOLIC KIRCHHOFF EQUATIONS

被引：2

作者：

Cao, Yang ^{[1
]}

Zhao, Qiuting ^{[1
]}

机构：

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

来源：

ELECTRONIC RESEARCH ARCHIVE | 2021年 / 29卷 / 06期

关键词：

Pseudo-parabolic; Kirchhoff equation; global existence; blow-up; BLOW-UP; GLOBAL EXISTENCE; POTENTIAL WELLS; TIME; FUNCTIONALS; EXPONENT;

D O I：

10.3934/era.2021064

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the initial boundary value problem for a mixed pseudo-parabolic Kirchhoff equation. Due to the comparison principle being invalid, we use the potential well method to give a threshold result of global existence and non-existence for the sign-changing weak solutions with initial energy J(u(0)) <= d. When the initial energy J(u(0)) > d, we find another criterion for the vanishing solution and blow-up solution. Our interest also lies in the discussion of the exponential decay rate of the global solution and life span of the blow-up solution.

引用

页码：3833 / 3851

页数：19

共 36 条

[1] Global Nonexistence for Nonlinear Kirchhoff Systems [J].

Autuori, Giuseppina ;

Pucci, Patrizia ;

Salvatori, Maria Cesarina .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 196 (02) :489-516

[2]

Brezis H, 2011, UNIVERSITEXT, P1

[3] BLOWUP IN A PARTIAL-DIFFERENTIAL EQUATION WITH CONSERVED 1ST INTEGRAL [J].

BUDD, C ;

DOLD, B ;

STUART, A .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1993, 53 (03) :718-742

[4] Asymptotic behavior of global solutions to a class of mixed pseudo-parabolic Kirchhoff equations [J].

Cao, Yang ;

Zhao, Qiuting .

APPLIED MATHEMATICS LETTERS, 2021, 118 (118)

[5] Robustness of nonautonomous attractors for a family of nonlocal reaction-diffusion equations without uniqueness [J].

Caraballo, Tomas ;

Herrera-Cobos, Marta ;

Marin-Rubio, Pedro .

NONLINEAR DYNAMICS, 2016, 84 (01) :35-50

[6] DIGITAL REMOVAL OF RANDOM MEDIA IMAGE DEGRADATIONS BY SOLVING DIFFUSION EQUATION BACKWARDS IN TIME [J].

CARASSO, AS ;

SANDERSON, JG ;

HYMAN, JM .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1978, 15 (02) :344-367

[7] GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS FOR INFINITELY DEGENERATE SEMILINEAR PSEUDO-PARABOLIC EQUATIONS WITH LOGARITHMIC NONLINEARITY [J].

Chen, Hua ;

Xu, Huiyang .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (02) :1185-1203

[8] Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity [J].

Chen, Sitong ;

Zhang, Binlin ;

Tang, Xianhua .

ADVANCES IN NONLINEAR ANALYSIS, 2020, 9 (01) :148-167

[9] Variable exponent, linear growth functionals in image restoration [J].

Chen, Yunmei ;

Levine, Stacey ;

Rao, Murali .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 66 (04) :1383-1406

[10] Global existence and blow-up for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity [J].

Ding, Hang ;

Zhou, Jun .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 478 (02) :393-420

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