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

Universitatea din Craiova. Analele. Seria: Matematica, Informatica

article

Mohammed Abdellaoui¹  Hicham Redwane² 

[1] LAMA, Faculty of Sciences Dhar El Mahraz, University of Fez, Department of Mathematics;Faculté des Sciences Juridiques, Économiques et Sociales, Université Hassan 1

关键词: Equivalence;    Nonlinear parabolic equations;    Variable exponentspaces;    p(·)-capacity;    Diffuse measure;    Entropy/Renormalized solutions;   

DOI  :  10.52846/ami.v50i1.1619

学科分类：社会科学、人文和艺术（综合）

来源: Universitatea din Craiova / University of Craiova

【 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" $p(\cdot)$-capacity, initial datum, and diffuse measure data (which does not charge the set of null $p(\cdot)$-capacity). Conditions, under which "generalized weak" solutions of the nonhomogeneous problem are in fact well-defined, are also given.

【 授权许可】

Unknown