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

页码：1803 / 1833

页数：31

共 50 条

[31] Regularity results for degenerate parabolic equations with Lm data
Mokhtari, F.
Khelifi, H.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2023, 68 (12) : 2001 - 2015
[32] Regularity of solutions of higher order nonlinear elliptic and parabolic equations
Skrypnik, IV
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (01) : 147 - 157
[33] Asymptotic behavior of solutions for nonlinear parabolic operators with natural growth term and measure data
Abdellaoui, M.
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2020, 11 (03) : 1289 - 1329
[34] On some regularity results of parabolic problems with nonlinear perturbed terms and general data
Abdellaoui, M.
Redwane, H.
PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2022, 3 (01):
[35] Asymptotic behavior for solutions to the vector nonlinear Schrodinger equations
Hoshino, Gaku
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 529 (01)
[36] Radon measure-valued solutions of nonlinear strongly degenerate parabolic equations
Porzio, Maria Michaela
Smarrazzo, Flavia
Tesei, Alberto
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2014, 51 (1-2) : 401 - 437
[37] Asymptotic Behavior of Solutions to Nonlinear Fractional Differential Equations
Kassim, Mohammed D.
Furati, Khaled M.
Tatar, Nasser-Eddine
MATHEMATICAL MODELLING AND ANALYSIS, 2016, 21 (05) : 610 - 629
[38] On the asymptotic behavior of solutions to inverse problems for parabolic equations
Vasin, IA
Kamynin, VL
SIBERIAN MATHEMATICAL JOURNAL, 1997, 38 (04) : 647 - 662
[39] Asymptotic behavior of solutions to a class of semilinear parabolic equations
Wei Guo
Xinyue Wang
Mingjun Zhou
Boundary Value Problems, 2016
[40] Existence and asymptotic behavior of Radon measure-valued solutions for a class of nonlinear parabolic equations
Quincy Stévène Nkombo
Fengquan Li
Christian Tathy
Advances in Difference Equations, 2021

← 1 2 3 4 5 →