Semilinear heat equation with singular terms

Author:

Ould Khatri Mohamed Mahmoud1,Youssfi Ahmed1ORCID

Affiliation:

1. Sidi Mohamed Ben Abdellah University

Abstract

The main goal of this paper is to analyze the existence and nonexistence as well as the regularity of positive solutions for the following initial parabolic problem { t u Δ u = μ u | x | 2 + f u σ in  Ω T := Ω × ( 0 , T ) , u = 0 on  Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in  Ω , where Ω R N , N 3 , is a bounded open, σ 0 and μ > 0 are real constants and f L m ( Ω T ) , m 1 , and u 0 are nonnegative functions. The study we lead shows that the existence of solutions depends on σ and the summability of the datum f as well as on the interplay between μ and the best constant in the Hardy inequality. Regularity results of solutions, when they exist, are also provided. Furthermore, we prove uniqueness of finite energy solutions.

Publisher

University of Szeged

Subject

Applied Mathematics

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3