On inverse source term for heat equation with memory term

Abstract

In this article, we first study the inverse source problem for parabolic with memory term. We show that our problem is ill-posed in the sense of Hadamard. Then, we construct the convergence result when the parameter tends to zero. We also investigate the regularized solution using the Fourier truncation method. The error estimate between the regularized solution and the exact solution is obtained.

Keywords

• inverse source problem
• parabolic equation
• memory term
• regularization method
• error estimate
• 35k99
• 47j06
• 47h10
• 35k05