Equivalence of "generalized" solutions for nonlinear parabolic equations with variable exponents and diffuse measure data

被引：0

作者：

Abdellaoui, Mohammed ^{[1
]}

Redwane, Hicham ^{[2
]}

机构：

[1] Sidi Mohamed Ben Abdellah Univ, Fac Sci Dhar El Mahraz, Dept Math, LAMA, BP 1796, Atlas Fez, Morocco

[2] Univ Hassan 1, Fac Sci Jurid Econ & Sociales, BP 764, Settat, Morocco

来源：

ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES | 2023年 / 50卷 / 01期

关键词：

Equivalence; Nonlinear parabolic equations; Variable exponent spaces; P(; )-capacity; Diffuse measure; Entropy; Renormalized solutions; RENORMALIZED SOLUTIONS; ELLIPTIC-EQUATIONS; SOBOLEV SPACES; ENTROPY SOLUTIONS; EXISTENCE; BOUNDARY; LEBESGUE; FUNCTIONALS; UNIQUENESS; CAPACITY;

D O I：

10.52846/ami.v50i1.1619

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

. We prove the equivalence of suitably defined weak solutions of a nonhomogeneous initial-boundary value problem for a class of nonlinear parabolic equations. We also develop the notion of both "renormalized" and "entropy" solutions with respect to the "generalized" P(& BULL;)-capacity, initial datum, and diffuse measure data (which does not charge the set of null P(& BULL;)-capacity). Conditions, under which "generalized weak" solutions of the nonhomogeneous problem are in fact well-defined, are also given.

引用

页码：60 / 90

页数：31

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