一类积分偏微分方程的Robin问题

On the Robin problem for a category of integral partial differential equation

研究带有Ｒｏｂｉｎ边界条件的一类积分偏微分方程的初边值问题，采用Ｖｏｌｔｅｒ－ｒａ积分方程理论及Ｇａｌｅｒｋｉｎ方法，首先建立了局部解的存在唯一性，通过积分估计证明了局部解可以扩展为一个关于初值稳定的整体强解．其结果补充和丰富了这类方程的原有结果．

Robin boundary and initial value problem in a category of integral partial differential equation is researched. The existence and uniqueness of local solution is established first by using Volterra integral equation theory and Galerkin method, and, then by integral estimate, the possibility of generalization of local solution into a global stability strong solution with global stability is proved. The research makes the relevant content in the discussed category of equation complemented and more completed.