具非线性来源项的抛物型方程反问题研究

An Parabolic Differential Equation Inverse Problem with a Nonlinear Source Term

本文主要研究一类具非线性来源项的抛物型方程,利用单调算子理论和Sobolev嵌入定理,证明了正问题解的存在性与唯一性。在合适的容许集中证明了反问题拟解的存在性。

This paper is devoted to a class of inverse problem for parabolic differential equation with a non-linear source term. Using the theories of monotone operator and the Sobolev embedding theorem, we verify the existence and uniqueness of weak solution for the direct problem as well as the ex-istence of quasi-solutions of the inverse source problem in an appropriate class of admissible source functions.