BLOWUP AND EXISTENCE OF GLOBAL SOLUTIONS TO NONLINEAR PARABOLIC EQUATIONS WITH DEGENERATE DIFFUSION

被引：0

作者：

Zhang, Zhengce ^{[1
]}

Li, Yan ^{[1
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年

基金：

中国国家自然科学基金;

关键词：

Degenerate parabolic equation; L-infinity blowup; gradient blowup; global solution; comparison principle; GRADIENT BLOWUP; HEAT-EQUATION; P-LAPLACIAN; NONEXISTENCE; CONVERGENCE; BOUNDARY;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider the degenerate parabolic equation u(t) - div(vertical bar del u vertical bar(p-2)del u) = lambda u(m) + mu vertical bar del u vertical bar(q) on a smoothly bounded domain Omega subset of R-N (N >= 2), with homogeneous Dirichlet boundary conditions. The values of p > 2, q; m; lambda and mu will vary in different circumstances, and the solutions will have different behaviors. Our main goal is to present the sufficient conditions for L-infinity blowup, for gradient blowup, and for the existence of global solutions. A general comparison principle is also established.

引用

页数：17

共 50 条

[41] ANALYSIS OF BLOWUP FOR A NONLINEAR DEGENERATE PARABOLIC EQUATION
CHEN, HW
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 192 (01) : 180 - 193
[42] Blowup behaviors for degenerate parabolic equations coupled via nonlinear boundary flux
Xiang, Zhaoyin
Mu, Chunlai
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2007, 6 (02) : 487 - 503
[43] Existence of solutions for nonlinear elliptic degenerate equations
Benkirane, A
Bennouna, J
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 54 (01) : 9 - 37
[44] Some sharp results about the global existence and blowup of solutions to a class of pseudo-parabolic equations
Zhu, Xiaoli
Li, Fuyi
Li, Yuhua
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2017, 147 (06) : 1311 - 1331
[45] Remarks on global existence and blowup for damped nonlinear Schrodinger equations
Ohta, Masahito
Todorova, Grozdena
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 23 (04) : 1313 - 1325
[46] Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients
Kwon, Dohyun
Meszaros, Alpar Richard
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2021, 104 (02): : 688 - 746
[47] BLOWUP AND GLOBAL EXISTENCE OF THE NONLINEAR SCHRODINGER EQUATIONS WITH MULTIPLE POTENTIALS
Gan, Zaihui
Guo, Boling
Zhang, Jian
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (04) : 1303 - 1312
[48] Existence for Nonautonomous Parabolic-Elliptic Degenerate Diffusion Equations
Favini, Angelo
Marinoschi, Gabriela
DEGENERATE NONLINEAR DIFFUSION EQUATIONS, 2012, 2049 : 91 - 108
[49] REMARKS ON GLOBAL EXISTENCE FOR NONLINEAR PARABOLIC EQUATIONS
ZHENG, SM
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1986, 10 (01) : 107 - 114
[50] Existence of Renormalized Solutions for Nonlinear Parabolic Equations
Akdim, Y.
Benkirane, A.
Elmoumni, M.
Redwane, H.
JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2014, 27 (01): : 28 - 49

← 1 2 3 4 5 →