Almost Periodic Type And Remotely Almost Periodic Type Solutions To Parabolic Inverse Problems

The paper consists of two parts: one part concerns on the applications of almost periodic type functions, the other part concerns on remotely almost periodic function and slowly oscillating function and their applications.Since H. Bohr proposed the theory of almost periodic function, this field has been developed greatly. A main feature in developing the theory is that the scope is expanding: from almost periodic function, asymptotically almost periodic function, weakly almost periodic function to pseudo almost periodic function which was introduced by Professor Zhang in 1992. Every extension consumedly enlarges the theory and their applications. The differential equations of almost periodic type are interested in the throry of mathematics and have broad prospects in practical applications. In this paper, incllusion to above-mentioned situations, some aspects of concrete work have been done to almost periodic type functions'application in parabolic partial differential equations.First, we extend almost periodic type functions and its properties to more general setting.Second, we investigate an almost periodic type solution of a geneal parabolic partial differential forward problem-initial value problem.Third, for some inverse problems of parabolic differential equations (some Cauchy problems and boundary value problem), we proved existence, uniquness and stability of the almost periodic type solutions.Nowadays power singal spaces are a subject that is concerned widely. An impotant power signal space is almost periodic functions space. But in practical applications such as in Rador, Optics, Robust Control, etc, real needs are to define new, large, nice spaces. For this purpose, from 2004 to 2006 Professor Zhang create uniform limit power function space and strong limit power function space that are large, nice spaces. It is important to exploit such spaces'applications in some areas, e. g. in differential equations, etc.