VISCOSITY SOLUTION THEORY OF A CLASS OF NONLINEAR DEGENERATE PARABOLIC EQUATIONS Ⅰ. UNIQUENESS AND EXISTENCE OF VISCOSITY SOLUTIONS

VISCOSITY SOLUTION THEORY OF A CLASS OF NONLINEAR DEGENERATE PARABOLIC EQUATIONS Ⅰ. UNIQUENESS AND EXISTENCE OF VISCOSITY SOLUTIONS

全文增补中

导出

摘要 In this part we construct a unique bounded Holder continuous viscosity solution for the nonlinear PDEs with the evolution p-Laplacian equation and its anisotropic version as typical examples. The existence and properties of free boundaries will be discussed in part Ⅱ. In this part we construct a unique bounded Holder continuous viscosity solution for the nonlinear PDEs with the evolution p-Laplacian equation and its anisotropic version as typical examples. The existence and properties of free boundaries will be discussed in part Ⅱ.

作者詹毅

出处《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1997年第2期136-144,共6页 应用数学学报（英文版）

关键词 DEGENERATE P-LAPLACIAN ANISOTROPIC viscosity solution Degenerate, p-Laplacian, anisotropic, viscosity solution

分类号 O175 [理学—基础数学]

引文网络
相关文献

参考文献15

1Robert Jensen.The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations[J]. Archive for Rational Mechanics and Analysis . 1988 (1)
2S. N. Kruzhkov.Results concerning the nature of the continuity of solutions of parabolic equations and some of their applications[J]. Mathematical Notes of the Academy of Sciences of the USSR . 1969 (1)
3V. Vespri.On the Local Behavior of Solutions of Certain Singular Parabolic Equations. Non. Anal.T.M.A . 1991
4Y. Giga,S. Goto,H. ISHII and M.-H. Sato.Comparison Principle and Convexity Preserving Propertiesfor Singular Degenerate Parabolic Equations on Unbounded Domains. Indiana University Mathematics Journal . 1991
5L.C. Evans and J. Spruck.Motion of Level Sets by Mean Curvature I. J. D. Geometry . 1991
6P.L. Lions and M.G. Crandall.Viscosity Solution of H-J Equations. Trans. AMS . 1983
7L.K. Martinson and K.B. Paplov.Unsteady Shear Flow of a Conducting Fluid with a RheologicalLaw. Magnit, Gidrodinamika . 1970
8E. Di Benndetto and M.A. Herrero.On the Cauchy Problem and initial Traces for a DegenerateParabolic Equation. Trans. A.M.S . 1989
9B.J. Bian and G.C. Dong.The Comparison Principle and Uniqueness of Viscosity Solutions of FullyNonlinear Second Order Parabolic Equations. Chinese Annals of Mathematics . 1990
10L.A. Caffarelli,J.L. Vazquez and W.I. Wolanski.Lipschitz Continuity of Solutions and Interfaces ofn-dimensional PME. Indiana University Mathematics Journal . 1987

共引文献1

1詹毅.VISCOSITY SOLUTION THEORY OF A CLASS OF NONLINEAR DEGENERATE PARABOLIC EQUATIONS Ⅱ. LIPSCHITZ CONTINUITY OF FREE BOUNDARY[J].Acta Mathematicae Applicatae Sinica,1997,13(3):235-242.

1LIANG ZhenGuo,YAN Jun.Regularity of viscosity solutions near KAM torus[J].Science China Mathematics,2008,51(3):361-368.
2LIU Zhenhai(Department of Mathematics, Changsha University of Electric Power,Changsha 410077, China).ON A NONLINEAR DEGENERATE PARABOLICEQUATION[J].Systems Science and Mathematical Sciences,1999,12(S1):122-128.
3詹毅.VISCOSITY SOLUTION THEORY OF A CLASS OF NONLINEAR DEGENERATE PARABOLIC EQUATIONS Ⅱ. LIPSCHITZ CONTINUITY OF FREE BOUNDARY[J].Acta Mathematicae Applicatae Sinica,1997,13(3):235-242.
4Deng Weibing Xie ChunhongDept.ofMath.,NanjingUniv.,Nanjing210093,China..A NONLINEAR DEGENERATE PARABOLIC EQUATION WITH NON-LOCAL SOURCE[J].Applied Mathematics(A Journal of Chinese Universities),2002,17(2):171-176.
5HONG Yiguang, YUNG Siupang, MEI Shengwei and QIN Huashu1. Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, China,2. Department of Mathematics, Hong Kong University, Hong Kong, China.Viscosity solution to nonlinear H_∞ control[J].Chinese Science Bulletin,1997,42(11):890-894.
6詹毅.THE BERNSTEIN ESTIMATES OF VISCOSITY SOLUTIONS OF LINEAR PARABOLIC EQUATIONS[J].Acta Mathematicae Applicatae Sinica,1995,11(3):255-262.
7VISCOSITY SOLUTIONS DEFINED BY RIGHT DIFFERENTIALS[J].Journal of Systems Science & Complexity,2002,15(2):146-154.
8CHENG Wei Department of Mathematics, Nanjing University, Nanjing 210093, China.Birkhoff's theorem and viscosity solutions of Hamilton-Jacobi equations[J].Science China Mathematics,2009,52(8):1796-1800.
9WeiAnLIU,GangLU.Viscosity Solutions of Monotonic Functional Parabolic PDE[J].Acta Mathematica Sinica,English Series,2004,20(4):739-748.
10Yu-dong SUN,Yi-min SHI,MIN WU.Nonexistence and Longtime Behaviors of Solutions to a Class of Nonlinear Degenerate Parabolic Equations Not in Divergence Form[J].Acta Mathematicae Applicatae Sinica,2016,32(2):327-332.

Acta Mathematicae Applicatae Sinica

1997年第2期

浏览历史

内容加载中请稍等...

VISCOSITY SOLUTION THEORY OF A CLASS OF NONLINEAR DEGENERATE PARABOLIC EQUATIONS Ⅰ. UNIQUENESS AND EXISTENCE OF VISCOSITY SOLUTIONS

参考文献15

共引文献1

相关作者

相关机构

相关主题

浏览历史