An energy formula for fully nonlinear degenerate parabolic equations in one spatial dimension

被引：1
|
作者：
Lappicy, Phillipo [1 ,2 ]
Beatriz, Ester [1 ]
机构：
[1] Univ Sao Paulo, ICMC, Ave Trab Sao Carlense 400, BR-13566590 Sao Carlos, Brazil
[2] Univ Complutense Madrid, Pl Ciencias 3, Madrid 28040, Spain
来源：
MATHEMATISCHE ANNALEN | 2024年 / 389卷 / 04期
基金：
巴西圣保罗研究基金会;
关键词：
35K65; 37L45; 35A15; 35A16; 35B38; HAMILTON-JACOBI EQUATION; POROUS-MEDIUM EQUATION; LYAPUNOV FUNCTION; GLOBAL-SOLUTIONS; STEADY-STATES; BLOW-UP; CONVERGENCE; BOUNDEDNESS;
D O I：
10.1007/s00208-023-02740-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Energy (or Lyapunov) functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano constructed a Lyapunov function for quasilinear non-degenerate parabolic equations. We modify Matano's method to construct an energy formula for fully nonlinear degenerate parabolic equations. We provide several examples of formulae, and in particular, a new energy candidate for the porous medium equation.
引用
收藏
页码：4125 / 4147
页数：23
相关论文
共 50 条
  • [1] Convergence for degenerate parabolic equations in one dimension
    Feireisl, E.
    Simondon, F.
    Comptes Rendus De L'Academie Des Sciences. Serie I, Mathematique, 323 (03):
  • [2] Convergence for degenerate parabolic equations in one dimension
    Feireisl, E
    Simondon, F
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1996, 323 (03): : 251 - 255
  • [3] Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension
    Burger, Raimund
    Ruiz, Ricardo
    Schneider, Kai
    Sepulveda, Mauricio
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2008, 42 (04): : 535 - 563
  • [4] A Lyapunov function for fully nonlinear parabolic equations in one spatial variable
    Phillipo Lappicy
    Bernold Fiedler
    São Paulo Journal of Mathematical Sciences, 2019, 13 : 283 - 291
  • [5] A Lyapunov function for fully nonlinear parabolic equations in one spatial variable
    Lappicy, Phillipo
    Fiedler, Bernold
    SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2019, 13 (01): : 283 - 291
  • [6] SINGULAR NEUMANN BOUNDARY PROBLEMS FOR A CLASS OF FULLY NONLINEAR PARABOLIC EQUATIONS IN ONE DIMENSION
    Kagaya, Takashi
    Liu, Qing
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2021, 53 (04) : 4350 - 4385
  • [7] Strong solutions of a class of fully nonlinear degenerate parabolic equations
    Li, Jing
    Yin, Jingxue
    Jin, Chunhua
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (08) : 2025 - 2037
  • [8] Classical solutions for a class of fully nonlinear degenerate parabolic equations
    Yin, Jingxue
    Li, Jing
    Jin, Chunhua
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 360 (01) : 119 - 129
  • [9] Multiresolution schemes for strongly degenerate parabolic equations in one space dimension
    Burger, Raimund
    Kozakevicius, Alice
    Sepulveda, Mauricio
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2007, 23 (03) : 706 - 730
  • [10] Nonlinear degenerate parabolic equations
    Liu, ZH
    ACTA MATHEMATICA HUNGARICA, 1997, 77 (1-2) : 147 - 157
12345