Kernel identification problem from an one-dimensional integrodifferential heat equation in a half-bounded domain

Аннотация

In this work, the inverse problem of determining the kernel of the integral entering in the one-dimensional integro-differential heat equation is considered. The direct problem is the initial-boundary problem for the this equation in the half-bounded straight line. An additional condition for solving the inverse problem is given the solution of direct problem on line 𝑥 = 0. At the beginning the inverse problem will be reduced to the equivalent auxiliary problem. Then this problem is replaced by the system of integral equations of the Volterra-type with respect to unknown functions. Further to this system the principle of contractive mapping in the space of continuous functions will be applied. As a result, the theorem on the global existence and uniqueness of the solution is proved.