Identification of memory kernels in one-dimensional Heat flow with boundary conditions of the third kind

摘要

An inverse problem for identification of memory kernels in one-dimensional heat flow with boundary conditions of the third kind is dealt with where the kernel is represented by a finite sum of products of known spatially-dependent functions and unknown time-dependent functions. As additional conditions for the inverse problem observations of temperature in given points are prescribed. The solutions of the direct and inverse problem are obtained by means of the Laplace transform method. The fixed point equations for these solutions are solved by the method of successive iterations via the contraction mapping property.