Weak inverse problems for parabolic integro-differential equations containing two kernels

Abstract

An inverse problem to determine a coefficient and two kernels in a parabolic integro-differential equation is considered. A corresponding direct problem is supposed to be in the weak form. Existence of the quasi-solution is proved and issues related to Frechet differentiation of the cost functional are treated.

Keywords

• Inverse problem
• parabolic integro-differential equation
• relaxation kernel
• quasi-solution