Existence And Uniqueness Of Solutions To Sublinear Heat Equations With Asymptotically Almost Periodic Coefficients

This paper studies the Dirichlet problem of the sublinear heat equation with time twhere ? is the bounded domain in RN with smooth boundaries(?)?,0<q<1.The full text is divided into three parts:In the first part we briefly introduces the development history of almost periodic function,the research status and main results of sublinear heat equation.In the second part we introduces the basic concepts of asymptotically almost periodic functions and sobolev space and other related content.In the third part we study the existence and uniqueness of asymptotically al-most periodic solution of equation(0.0.2)when f has asymptotically almost periodic solution by method of subsolutions and supersolutions.