Critical Curves of Solutions in Nonlinear Parabolic Equations Involving p, m-Laplace Operators

被引：2

作者：

Liu, Bingchen ^{[1
]}

Zhang, Q. ^{[1
]}

Zhang, X. ^{[1
]}

Zhao, Z. ^{[2
]}

机构：

[1] China Univ Petr, Coll Sci, Qingdao 266580, Shandong, Peoples R China

[2] Beijing Inst Technol, Sch Informat & Elect, Beijing 100081, Peoples R China

来源：

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2018年 / 44卷 / 06期

关键词：

p; m-Laplace equation; Critical global-existence curve; Critical Fujita's curve; Blow-up; BLOW-UP; CRITICAL EXPONENTS;

D O I：

10.1007/s41980-018-0098-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study some nonlinear parabolic equation involving p, m-Laplace operator with nonlinear source and boundary flux. First, we determine the critical curve of the existence of global solutions by constructing self-similar auxiliary functions. Second, the exponent region is proposed where every nontrivial solution blows up in finite time. In addition, blow-up phenomenon of the Fujita type is proved for the corresponding Cauchy problem of the nonlinear parabolic equation.

引用

页码：1427 / 1447

页数：21

共 50 条

[41] On degenerate p(x)-Laplace equations involving critical growth with two parameters
Ho, Ky
Sim, Inbo
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 132 : 95 - 114
[42] Schrodinger p()-Laplace equations in RN involving indefinite weights and critical growth
Ky Ho
Kim, Yun-Ho
Lee, Jongrak
JOURNAL OF MATHEMATICAL PHYSICS, 2021, 62 (11)
[43] Existence results for Schrodinger p(.)-Laplace equations involving critical growth in RN
Ho, Ky
Kim, Yun-Ho
Sim, Inbo
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 182 : 20 - 44
[44] Liouville results for m-Laplace equations of Lane-Emden-Fowler type
Damascelli, Lucio
Farina, Alberto
Sciunzi, Berardino
Valdinoci, Enrico
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2009, 26 (04): : 1099 - 1119
[45] Numerical solution of a class of singular free boundary problems involving the m-Laplace operator
Morgado, L.
Lima, P.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (09) : 2838 - 2847
[46] A critical behavior for some semilinear parabolic equations involving sign changing solutions
Zhang, QS
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 50 (07) : 967 - 980
[47] A WEAK MAXIMUM PRINCIPLE FOR THE LINEARIZED OPERATOR OF m-LAPLACE EQUATIONS WITH APPLICATIONS TO A NONDEGENERACY RESULT
Sciunzi, Berardino
ADVANCES IN DIFFERENTIAL EQUATIONS, 2005, 10 (02) : 223 - 240
[48] Linking solutions for p-Laplace equations with nonlinearity at critical growth
Degiovanni, Marco
Lancelotti, Sergio
JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (11) : 3643 - 3659
[49] Linking solutions for quasilinear equations at critical growth involving the “1-Laplace” operator
Marco Degiovanni
Paola Magrone
Calculus of Variations and Partial Differential Equations, 2009, 36
[50] Linking solutions for quasilinear equations at critical growth involving the "1-Laplace" operator
Degiovanni, Marco
Magrone, Paola
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2009, 36 (04) : 591 - 609

← 1 2 3 4 5 →