INTERIOR DERIVATIVE BLOW-UP FOR QUASILINEAR PARABOLIC EQUATIONS

被引：33

作者：

Giga, Yoshikazu ^{[1
]}

机构：

[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 060, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 1995年 / 1卷 / 03期

关键词：

D O I：

10.3934/dcds.1995.1.449

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give examples of a bounded solution whose gradient blows up in a finite time but it stays bounded on the boundary for a class of quasilinear parabolic equations with zero boundary data. The method reflects a geometric argument for curve evolution equations.

引用

页码：449 / 461

页数：13

共 16 条

[1]

Angenent S. B., INTERIOR GRADIENT BL

[2] ON THE REGULARITY OF THE SOLUTIONS OF SOME DEGENERATE PARABOLIC EQUATIONS [J].

BLANC, P .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (5-6) :821-846

[3]

CHEN YG, 1991, DIFF GEOMETRY, V33, P749

[4] USERS GUIDE TO VISCOSITY SOLUTIONS OF 2ND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS [J].

CRANDALL, MG ;

ISHII, H ;

LIONS, PL .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 27 (01) :1-67

[5]

Dlotko T., 1994, J MATH ANAL APPL, V154, P226

[6]

Edmunds D. E., 1971, ANN SCUOLA NORM SUP, V25, P397

[7]

Evans L. C., GEOMETRIC INTERPRETA

[8] MOTION OF LEVEL SETS BY MEAN-CURVATURE .1. [J].

EVANS, LC ;

SPRUCK, J .

JOURNAL OF DIFFERENTIAL GEOMETRY, 1991, 33 (03) :635-681

[9]

Fila M., 1994, DIFFERENTIAL INTEGRA, V7, P811

[10] GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR INTERFACE EQUATIONS COUPLED WITH DIFFUSION-EQUATIONS [J].

GIGA, Y ;

GOTO, S ;

ISHII, H .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1992, 23 (04) :821-835

← 1 2 →