Regularity of Viscous Solutions for a Degenerate Non-linear Cauchy Problem

被引：0

作者：

Hernandez-Sastoque, Eric ^{[1
]}

Klingenberg, Christian ^{[2
]}

Rendon, Leonardo ^{[3
]}

Juajibioy, Juan C. ^{[4
]}

机构：

[1] Univ Magdalena, Dept Matemat, Santa Marta, Colombia

[2] Univ Wurzburg, Dept Math, Wurzburg, Germany

[3] Univ Nacl Colombia, Dept Matemat, Bogota, Colombia

[4] Fdn Univ Autonoma Colombia, Dept Ciencias Nat & Exactas, Bogota, Colombia

来源：

JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS | 2016年 / 29卷 / 01期

关键词：

Viscosity solution; Holder estimates; Holder continuity;

D O I：

10.4208/jpde.v29.n1.2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problemfor a class of nonlinear degenerate parabolic equation with forcing. By using the vanishing viscosity method it is possible to construct a generalized solution. Moreover, this solution is a Lipschitz function on the spatial variable and Holder continuous with exponent 1/2 on the temporal variable.

引用

页码：14 / 21

页数：8

共 50 条

[1] A DEGENERATE NON-LINEAR CAUCHY-PROBLEM
KUTTLER, KL
[J]. APPLICABLE ANALYSIS, 1982, 13 (04) : 307 - 322
[2] ON THE CAUCHY-PROBLEM FOR NON-LINEAR DEGENERATE HYPERBOLIC EQUATION
GUAN, CQ
SUN, HS
[J]. KEXUE TONGBAO, 1983, 28 (06): : 734 - 739
[3] Regularity of viscosity solutions to a degenerate nonlinear Cauchy problem
Zhao, Yan-Yan
Chen, Zu-Chi
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (04) : 741 - 746
[4] Long lifespan of solutions to a non-linear Cauchy problem
Gourdin, D
Mechab, M
[J]. JEAN LERAY '99 CONFERENCE PROCEEDINGS: THE KARLSKRONA CONFERENCE IN HONOR OF JEAN LERAY, 2003, 24 : 65 - +
[5] STABILIZATION OF SOLUTIONS OF A DEGENERATE NON-LINEAR DIFFUSION PROBLEM
ARONSON, D
CRANDALL, MG
PELETIER, LA
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1982, 6 (10) : 1001 - 1022
[6] ON STABILIZATION OF SOLUTIONS OF THE CAUCHY PROBLEM FOR LINEAR DEGENERATE PARABOLIC EQUATIONS
Eidelman, S. D.
Kamin, S.
Tedeev, A. F.
[J]. ADVANCES IN DIFFERENTIAL EQUATIONS, 2009, 14 (7-8) : 621 - 641
[7] BOUNDARY REGULARITY FOR SOME NON-LINEAR ELLIPTIC DEGENERATE EQUATIONS
BREZIS, H
LIONS, PL
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1979, 70 (02) : 181 - 185
[8] C1,α regularity of solutions of some degenerate fully non-linear elliptic equations
Imbert, C.
Silvestre, L.
[J]. ADVANCES IN MATHEMATICS, 2013, 233 (01) : 196 - 206
[9] AN ELASTICITY PROBLEM WITH NON-LINEAR VISCOUS FRICTION
LICHT, C
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1984, 299 (07): : 277 - 280
[10] On critical exponents for weak solutions of the Cauchy problem for a non-linear equation of composite type
Korpusov, M. O.
Matveeva, A. K.
[J]. IZVESTIYA MATHEMATICS, 2021, 85 (04) : 705 - 744

← 1 2 3 4 5 →