Existence and non-existence of global solutions of pseudo-parabolic equations involving p(x)-Laplacian and logarithmic nonlinearity

被引：3

作者：

Van Chuong, Quach ^{[1
,2
,3
]}

Nhan, Le Cong ^{[4
]}

Truong, Le Xuan ^{[5
]}

机构：

[1] Univ Sci, Fac Math & Comp Sci, Ho Chi Minh City, Vietnam

[2] Vietnam Natl Univ, Ho Chi Minh City, Vietnam

[3] Dong Nai Univ, Dept Math, Bien Hoa, Dong Nai, Vietnam

[4] Ho Chi Minh City Univ Technol & Educ, Fac Appl Sci, Ho Chi Minh City, Vietnam

[5] Univ Econ Ho Chi Minh City UEH, Dept Math & Stat, Ho Chi Minh City, Vietnam

来源：

JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS | 2022年 / 8卷 / 01期

关键词：

Pseudo-parabolic p(x)-Laplacian equation; Logarithmic nonlinearity; Blow-up; Decay; LAPLACIAN EVOLUTION-EQUATIONS; TIME BLOW-UP; SOBOLEV EMBEDDINGS; VARIABLE EXPONENT; SPACES; FUNCTIONALS; STABILITY;

D O I：

10.1007/s41808-022-00162-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider a class of pseudo-parabolic equations involving p(x)-Laplacian and logarithmic nonlinearity. By using the potential well method, we give some threshold results on existence or nonexistence of global weak solutions when the initial energy is subcritical. Moreover, the decay estimates for the global bounded solutions and the growth estimates for the global unbounded solutions are also concerned.

引用

页码：483 / 512

页数：30

共 36 条

[1] Regularity results for stationary electro-rheological fluids
Acerbi, E
Mingione, G
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 164 (03) : 213 - 259
[2] Regularity results for a class of functionals with non-standard growth
Acerbi, E
Mingione, G
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 156 (02) : 121 - 140
[3] [Anonymous], 2018, Electron. J. Differ. Equ
[4] Barenblatt G.E., 1960, J APPL MATH USSR, V24, P12861303, DOI [10.1016/0021-8928(60)90107-6, DOI 10.1016/0021-8928(60)90107-6]
[5] MODEL EQUATIONS FOR LONG WAVES IN NONLINEAR DISPERSIVE SYSTEMS
BENJAMIN, TB
BONA, JL
MAHONY, JJ
[J]. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1972, 272 (1220) : 47 - +
[6] Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity
Chen, Hua
Tian, Shuying
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 258 (12) : 4424 - 4442
[7] Global solution and blow-up of a semilinear heat equation with logarithmic nonlinearity
Chen, Hua
Luo, Peng
Liu, Gongwei
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 422 (01) : 84 - 98
[8] Variable exponent, linear growth functionals in image restoration
Chen, Yunmei
Levine, Stacey
Rao, Murali
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 66 (04) : 1383 - 1406
[9] Blow-up phenomena for a pseudo-parabolic equation with p-Laplacian and logarithmic nonlinearity terms
Dai, Pan
Mu, Chunlai
Xu, Guangyu
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 481 (01)
[10] Lebesgue and Sobolev Spaces with Variable Exponents
Diening, Lars
Harjulehto, Petteri
Hasto, Peter
Ruzicka, Michael
[J]. LEBESGUE AND SOBOLEV SPACES WITH VARIABLE EXPONENTS, 2011, 2017 : 1 - +

← 1 2 3 4 →