Gradient blow-up solution with small initial datum for a Hamilton-Jacobi equation with degenerate diffusion

被引：0

作者：

Wang, Zhiyong ^{[1
,2
]}

Yin, Jingxue ^{[3
]}

机构：

[1] Fujian Normal Univ, Coll Math & Informat, Fuzhou 350117, Fujian, Peoples R China

[2] Fujian Normal Univ, Fujian Key Lab Math Anal & Applicat, Fuzhou 350117, Fujian, Peoples R China

[3] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 472卷 / 02期

关键词：

Gradient blow-up; Degenerate Hamilton-Jacobi equation; CRITICAL EXPONENTS; GLOBAL-SOLUTIONS; BOUNDEDNESS; BOUNDARY;

D O I：

10.1016/j.jmaa.2018.12.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the gradient blow-up phenomena for a Hamilton-Jacobi equation with degenerate diffusion u(t) = (vertical bar u(x)vertical bar(p-2)u(x))(x) + vertical bar u(x)vertical bar(q) in an interval for q > p >= 2. In the main theorem, we construct a gradient blow-up solution with a small L-1 initial datum. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：1914 / 1926

页数：13

共 50 条

[31] Gradient blowup rate for a viscous Hamilton–Jacobi equation with degenerate diffusion
Zhengce Zhang
Archiv der Mathematik, 2013, 100 : 361 - 367
[32] Blow-up for quasilinear heat equations described by means of nonlinear Hamilton-Jacobi equations
Galaktionov, VA
Vazquez, JL
JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 127 (01) : 1 - 40
[33] Finite Time vs. Infinite Time Gradient Blow-up in a Degenerate Diffusion Equation
Stinner, Christian
Winkler, Michael
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (05) : 2321 - 2354
[34] Blow-up in a degenerate parabolic equation
Winkler, M
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2004, 53 (05) : 1415 - 1442
[35] Infinite-time gradient blow-up in a degenerate parabolic equation
Winkler, Michael
INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS, 2012, 4 (1-2) : 126 - 153
[36] On Approximation of Multivalued Solution for Hamilton-Jacobi equation
Kolpakova, Ekaterina A.
IFAC PAPERSONLINE, 2018, 51 (32): : 805 - 809
[37] TREE GRAPHS AND THE SOLUTION TO THE HAMILTON-JACOBI EQUATION
MOLZAHN, FH
OSBORN, TA
JOURNAL OF MATHEMATICAL PHYSICS, 1986, 27 (01) : 88 - 99
[38] EXISTENCE OF A MAXIMUM SOLUTION OF HAMILTON-JACOBI EQUATION
GONZALEZ, R
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1976, 282 (22): : 1287 - 1290
[39] Blow-up phenomena for a doubly degenerate equation with positive initial energy
Mu, Chunlai
Zeng, Rong
Chen, Botao
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (02) : 782 - 793
[40] Approximation of a Multivalued Solution of the Hamilton-Jacobi Equation
Kolpakova, E. A.
MATHEMATICAL NOTES, 2020, 108 (1-2) : 77 - 86

← 1 2 3 4 5 →