Inverse Problem for an Abstract Nonlinear Parabolic Integrodifferential Equation

摘要

The authors consider a nonlinear abstract parabolic integrodifferential equationhaving a pair of time-dependent kernels which are unknown. The authors want to recover such kernels by using overdetermined data. The authors prove a local (in time) existence and uniqueness result. This result is obtained by using the analytic semigroup theory to reduce the inverse problem to a system of nonlinear Volterra equations of the second kind. Then the equivalent problem is solved via Contraction Principle. Moreover, an application to the nonlinear heat conduction with memory is shown.