Nonlinear parabolic equation having nonstandard growth condition with respect to the gradient and variable exponent

Opuscula Mathematica

article

Abderrahim Charkaoui (corresponding author)¹  Houda Fahim¹  Nour Eddine Alaa¹ 

[1] Laboratory LAMAI, Faculty of Science and Technology of Marrakech

关键词: variable exponent;    quasilinear equation;    Schaeffer's fixed point;    subsolution;    supersolution;    weak solution.;   

DOI  :  10.7494/OpMath.2021.41.1.25

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

We are concerned with the existence of solutions to a class of quasilinear parabolic equations having critical growth nonlinearity with respect to the gradient and variable exponent. Using Schaeffer's fixed point theorem combined with the sub- and supersolution method, we prove the existence results of a weak solutions to the considered problems.

【 授权许可】

CC BY-NC