Existence via time discretization for a class of doubly nonlinear operator-differential equations of Barenblatt-type

被引：2

作者：

Emmrich, Etienne ^{[1
]}

Vallet, Guy ^{[2
]}

机构：

[1] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

[2] CNRS, UMR 5142, Lab Math & Applicat Pau, F-64013 Pau, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 254卷 / 06期

关键词：

Nonlinear evolution equation; Barenblatt equation; Monotone operator; Existence of weak solution; Convergence of time discretization;

D O I：

10.1016/j.jde.2012.12.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The initial value problem for a first order operator-differential equation of type M(u') A(u, u') = f is studied, where both M and A are nonlinear operators. The equation can be interpreted as the quasistatic limit of a second order evolution equation with a severe coupling of the damping and nondamping term. Existence of a global-in-time weak solution is shown by proving convergence of a suitable time discretization method. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：2499 / 2514

页数：16

共 22 条

[11] Doubly nonlinear evolution equations of second order: Existence and fully discrete approximation [J].

Emmrich, Etienne ;

Thalhammer, Mechthild .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 251 (01) :82-118

[12] SYSTEMS OF NONLINEAR-WAVE EQUATIONS WITH NONLINEAR VISCOSITY [J].

FRIEDMAN, A ;

NECAS, J .

PACIFIC JOURNAL OF MATHEMATICS, 1988, 135 (01) :29-55

[13]

Gajewski H., 1974, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen

[14]

Gripenberg G., 1990, Encyclopedia of Mathematics and its Applications

[15]

Hokkanen V.-M, 2002, CHAPMAN HALL CRC RES, V432

[16]

KOVACIK O, 1991, CZECH MATH J, V41, P592

[17]

Lindqvist Peter, 2017, NOTES P LAPLACE EQUA

[18]

Lions J.-L., 1965, Bull. Soc. Math. Fr., V93, P43

[19]

Pruss J., 1993, EVOLUTIONARY INTEGRA, DOI 10.1007/978-3-0348-8570-6

[20]

Ptashnyk M, 2004, THESIS U HEIDELBERG

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