Uniformly bounded weak and classical solutions to a singular parabolic system and applications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:490

Article

Salmaniw, Yurij¹ 

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2R3, Canada

关键词: Singular parabolic systems;    Coupled parabolic equations;    Singular nonlinearity;    Dirichlet problems;    Bounded solutions;    Global solutions;   

DOI  :  10.1016/j.jmaa.2020.124200

来源: Elsevier

【 摘 要 】

Equations of both elliptic and parabolic type featuring singular nonlinearities have appeared in numerous works throughout the years. In this work, we consider a time dependent problem featuring nonlinearities of the form u(-p)v(-q), u(-r)v(-s) subject to homogeneous Dirichlet boundary conditions and prove the existence of uniformly bounded weak and classical solutions under appropriate conditions on p, q, r, s. These results can, in some ways, be seen as a generalization of the results presented in [9]. These results are obtained using a functional method motivated by works found in [8], [22], [6] etc., and the boundary behaviour of a fundamental singular elliptic equation described in [16]. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free