一类具有奇异项的半线性抛物方程解的研究  

Study on the solution of a class ofsemilinear parabolic equations with singular term

作　　者：贾文旭 高艳超 JIA Wen-xu;GAO Yan-chao(School of Mathematics and Statistics,Changchun University of Science and Technology,Changchun 130012,China)

机构地区：[1]长春理工大学数学与统计学院,吉林长春130012

出　　处：《东北师大学报（自然科学版）》2024年第3期33-38,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：吉林省科技发展计划项目(YDZJ202201ZYTS584);国家自然科学基金资助项目(12171054).

摘　　要：研究了一类具有奇异项和对数源的半线性抛物方程初边值问题.利用正则化方法处理了奇异项带来的困难,结合截断函数逼近得到了弱解的局部存在性;借助对数型Sobolev不等式和位势井方法,在临界和亚临界情形下证明了弱解的整体存在性;利用位势井族和微分不等式给出了整体解的衰退估计.The initial boundary value problem for a class of semilinear parabolic equations with singular term and logarithmic source is considered.The difficulty of dealing with singular term by regularization method,the local existence of the weak solution is obtained by approximating the truncation function.By means of logarithmic Sobolev inequality and potential well method,the global existence of the weak solution is proved in critical and subcritical cases.The decay estimation of the global solution is given by using the potential well family and differential inequality.

关 键 词：奇异项 对数源 位势井 存在性 

分 类 号：O175.8[理学—数学]