具强非线性耦合源的退化拋物方程组的Cauchy问题  

Cauchy Problem for Degenerate Parabolic System with Strongly Nonlinear Sources

作　　者：杜美华 DU MEIHUA(Department of Basic Courses,Qingdao University of Technology,Qindao College,Qingdao 266106,China)

机构地区：[1]青岛理工大学琴岛学院基础部,青岛266106

出　　处：《应用数学学报》2020年第6期939-948,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11201124)资助项目。

摘　　要：本文研究了一类具强非线性耦合源的退化抛物方程组的Cauchy问题,其中初值为Radon测度.我们得到的主要结果有两个:首先,利用先验估计和方程组的结构,我们克服了方程组主部的退化性与强非线性耦合源相互作用带来的困难,对该问题得到了解的存在性;其次,通过选取恰当的检验函数,我们证明了测度初值解的存在性在所考虑的类中是最优的.本文所得到的结果改进了已有的研究结果.This paper is devoted to the existence of solutions to the Cauchy problem of a class of degenerate parabolic system with strongly nonlinear coupled sources and initial data Radon measures.We obtain two main results.The first result is the existence of solutions to the Cauchy problem.To this end,we make full use of the methods of a priori estimates and the special structure of the degenerate parabolic system to overcome the difficulties which come from the interaction of the degeneracy of the principal parts of the degenerate parabolic system and the strongly nonlinear coupled sources in the system.The second result is to prove the existence of solutions of the Cauchy problem obtained in the first result is actually optimal in the class considered here by selecting the proper test functions.We remark that the results obtained in this paper improve the known existence results in this direction.

关 键 词：退化抛物方程组 CAUCHY问题 非线性耦合源 测度初值 

分 类 号：O175.2[理学—数学]