Asymptotic behavior and regularity properties of strongly nonlinear parabolic equations

被引：6
|
作者：
Porzio, Maria Michaela [1 ]
机构：
[1] Sapienza Univ Roma, Dipartimento Matemat Guido Castelnuovo, Piazzale A Moro 2, I-00185 Rome, Italy
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 2019年 / 198卷 / 05期
关键词：
Decay estimates; Asymptotic behavior; Regularity of solutions; p-Laplacian equation; Nonlinear degenerate parabolic equations; Smoothing effect; 35K10; 35K55; 35K65; 35K58; RENORMALIZED SOLUTIONS; EXISTENCE; DEGENERATE; UNIQUENESS; UNIFORM; BOUNDS;
D O I：
10.1007/s10231-019-00845-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study a class of nonlinear parabolic problems including the p-Laplacian equation. The initial datum and the forcing term are allowed to be summable functions or Radon measures. We prove that these equations have surprising regularizing properties. Moreover, we study the behavior in time of these solutions proving that decay estimates hold true also for nonzero reaction terms. Finally, we study the autonomous case.
引用
收藏
页码：1803 / 1833
页数：31
相关论文
共 50 条
  • [31] A refined asymptotic behavior of traveling wave solutions for degenerate nonlinear parabolic equations
    Ichida, Yu
    Matsue, Kaname
    Sakamoto, Takashi Okuda
    JSIAM LETTERS, 2020, 12 : 65 - 68
  • [32] Extinction and asymptotic behavior of solutions for nonlinear parabolic equations with variable exponent of nonlinearity
    Yanchao Gao
    Wenjie Gao
    Boundary Value Problems, 2013
  • [33] On the asymptotic behaviour of solutions of nonlinear parabolic equations
    Kon'kov, A
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2006, 136 : 365 - 384
  • [34] Some asymptotic methods for strongly nonlinear equations
    He, Ji-Huan
    INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2006, 20 (10): : 1141 - 1199
  • [35] Regularity in Sobolev spaces for doubly nonlinear parabolic equations
    Ebmeyer, C
    Urbano, JM
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 187 (02) : 375 - 390
  • [36] Interior Sobolev regularity for fully nonlinear parabolic equations
    Ricardo Castillo
    Edgard A. Pimentel
    Calculus of Variations and Partial Differential Equations, 2017, 56
  • [37] EXISTENCE AND REGULARITY RESULTS FOR SOLUTIONS TO NONLINEAR PARABOLIC EQUATIONS
    Grenon, Nathalie
    Mercaldo, Anna
    ADVANCES IN DIFFERENTIAL EQUATIONS, 2005, 10 (09) : 1007 - 1034
  • [38] Interior Sobolev regularity for fully nonlinear parabolic equations
    Castillo, Ricardo
    Pimentel, Edgard A.
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2017, 56 (05)
  • [39] Optimal regularity estimates for general nonlinear parabolic equations
    Byun, Sun-Sig
    Palagachev, Dian K.
    Shin, Pilsoo
    MANUSCRIPTA MATHEMATICA, 2020, 162 (1-2) : 67 - 98
  • [40] Optimal regularity estimates for general nonlinear parabolic equations
    Sun-Sig Byun
    Dian K. Palagachev
    Pilsoo Shin
    manuscripta mathematica, 2020, 162 : 67 - 98
12345