Parabolic Boundary Value Problem With Equivalued Surface On The Domain With Thin Layer

Boundary value problem with equivalued surface is a kind of non-local boundaryvalue problem,and it is put forward in 1970's.Recently Li Ta-tsien and his parteners do alot of work on this aspect.And motivated by many important applications,especially by re-sistivity well-logging in petroleum exploitation,Li Ta-tsien constructed the correspondingboundary value problems with equivalued surface of elliptic equations.This paper deals with certain kind of parabolic boundary value problem with equiv-alued surface on the domain with thin lever. Existence and uniqueness of solutions aregiven, and the limit behavior of solutions is also studied in this paper.In chapter 1 the background and history for the studied problem are given.In chapter 2 we shall give the proof of existence and uniqueness of solution to thestudied problem.In chapter 3 we study the boundary value problem with equivalued interface ofparabolic equation.In chapter 4 we give the limit behavior of solutions to the studied problem.