Uniqueness of the kernel determination problem in an integro-differential parabolic equation with variable coefficient

Abstract

Abstract. We investigate the inverse problem of determining the time and space dependent kernel of the integral term in the n-dimensional integro-differential equation of heat conduction from the known solution of the Cauchy problem for this equation. First, the original problem is replaced by the equivalent problem where an additional condition contains the unknown kernel without integral. We study the question of the uniqueness of the determining of this kernel. Next, assuming that there are two solutions k1(x, t) and k2(x, t) of the stated problem, it is formed an equation for the difference of this solution. Further research is being conducted for the difference k1(x, t) - k2(x, t) of solutions of the problem and using the techniques of integral equations estimates.