Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities

被引：12

作者：

Bertsch, Michiel ^{[1
,2
]}

Smarrazzo, Flavia ^{[3
]}

Tesei, Alberto ^{[3
]}

机构：

[1] CNR, Ist Applicaz Calcolo M Picone, Via Taurini 19, I-00185 Rome, Italy

[2] Univ Roma Tor Vergata, Rome, Italy

[3] Univ Roma La Sapienza, Dipartimento Matemat G Castelnuovo, Ple A Moro 5, I-00185 Rome, Italy

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2016年 / 712卷

关键词：

PSEUDOPARABOLIC REGULARIZATION; CONVERGENCE; MODEL; HEAT;

D O I：

10.1515/crelle-2013-0123

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a quasilinear parabolic equation of forward-backward type, under assumptions on the nonlinearity which hold for a wide class of mathematical models, using a pseudo-parabolic regularization of power type. We prove existence and uniqueness of positive solutions of the regularized problem in a space of Radon measures. It is shown that these solutions satisfy suitable entropy inequalities. We also study their qualitative properties, in particular proving that the singular part of the solution with respect to the Lebesgue measure is constant in time.

引用

页码：51 / 80

页数：30

共 50 条

[21] Further existence results for elliptic-parabolic and forward-backward parabolic equations
Paronetto, Fabio
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2020, 59 (04)
[22] On Lipschitz solutions for some forward-backward parabolic equations
Kim, Seonghak
Yan, Baisheng
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2018, 35 (01): : 65 - 100
[23] Forward-backward parabolic equations and their time delay approximations
Horstmann, D
EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS, 2005, : 1089 - 1091
[24] AN APPARENTLY UNNATURAL ESTIMATE ABOUT FORWARD-BACKWARD PARABOLIC EQUATIONS
Paronetto, Fabio
ADVANCES IN DIFFERENTIAL EQUATIONS, 2021, 26 (3-4) : 133 - 162
[25] Forward-backward stochastic differential equations and quasilinear parabolic PDEs
Pardoux, E
Tang, SJ
PROBABILITY THEORY AND RELATED FIELDS, 1999, 114 (02) : 123 - 150
[26] Forward-backward stochastic differential equations and quasilinear parabolic PDEs
Etienne Pardoux
Shanjian Tang
Probability Theory and Related Fields, 1999, 114 : 123 - 150
[27] Singular Perturbations of Forward-Backward p-Parabolic Equations
Antontsev S.N.
Kuznetsov I.V.
Journal of Elliptic and Parabolic Equations, 2016, 2 (1-2) : 357 - 370
[28] Regularizations of forward-backward parabolic PDEs
Geldhauser, Carina
GAMM Mitteilungen, 2024, 47 (04)
[29] Degenerate Regularization of Forward–Backward Parabolic Equations: The Regularized Problem
Flavia Smarrazzo
Alberto Tesei
Archive for Rational Mechanics and Analysis, 2012, 204 : 85 - 139
[30] Sobolev regularization of a class of forward backward-parabolic equations
Bui Le Trong Thanh
Smarrazzo, Flavia
Tesei, Alberto
JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (05) : 1403 - 1456

← 1 2 3 4 5 →