Well-posedness of a non-local abstract Cauchy problem with a singular integral  

作　　者：Haiyan JIANG Tiao LU Xiangjiang ZHU 

机构地区：[1]Introduction We consider the following initial value problem for the unknown functions c(t) and z): 1 School of Mathematical Sciences, Beijing Institute of Technology, Beijing 100081, China [2]School of Mathematical Sciences, Peking University, Beijing 100871, China [3]CAPT, HEDPS, LMAM, IFSA Collaborative Innovation Center of MoE, Peking University, Beijing 100871, China

出　　处：《Frontiers of Mathematics in China》2019年第1期77-93,共17页中国高等学校学术文摘·数学（英文）

基　　金：National Natural Science Foundation of China (Grant Nos. 1167103& 91630130, 91434201, 11421101).

摘　　要：A non-local abstract Cauchy problem with a singular integral is studied, which is a closed system of two evolution equations for a real-valued function and a function-valued function. By proposing an appropriate Banach space, the well-posedness of the evolution system is proved under some boundedness and smoothness conditions on the coefficient functions. Furthermore, an isomorphism is established to extend the result to a partial integro-differential equation with a singular convolution kernel, which is a generalized form of the stationary Wigner equation. Our investigation considerably improves the understanding of the open problem concerning the well-posedness of the stationary Wigner equation with in ow boundary conditions.

关 键 词：Partial integro-differential EQUATION (PIDE) SINGULAR integral WELLPOSEDNESS WIGNER EQUATION 

分 类 号：O[理学]