一类具时变系数源项的奇异伪抛物方程解的局部适定性  

Local Well-Posedness of Solution for a Singular Pseudo-Parabolic Equation with Time-Varying Coefficient Source Term

作　　者：甄鑫婷 王建[1] Zhen Xinting;Wang Jian(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2022年第S01期76-82,共7页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(11671188)资助。

摘　　要：本文研究具有时变系数源项和位势项的半线性奇异伪抛物方程Dirichlet初边值问题解的局部适定性。在位势项的系数变号情形下,结合Hardy不等式、截断技巧、Galerkin逼近技巧及压缩映像原理证明了问题局部解的存在性及唯一性。This article investigates the local well-posedness of Dirichlet initial boundary value problem for a singular pseudo-parabolic equation with time-varying coefficient source and potential terms. When the coefficient of the potential term changes sign, combining Hardy inequality, cut-off technique, Galerkin approximation method and contraction mapping principle, the existence and uniqueness of the local solution to the problem are proved.

关 键 词：奇异伪抛物方程 时变系数 位势 适定性 

分 类 号：O175[理学—数学]