INVERSE PROBLEM FOR INTEGRO-DIFFERENTIAL HEAT EQUATION WI TION WITH A VARIABLE COEFFICIEN ABLE COEFFICIENT OF THERM T OF THERMAL CONDUCTIVITY

Background. The inverse problem of finding a multidimensional memory kernel of a time convolution integral depending on a time variable t and (n-1)-dimensional spatial variable. 2-dimensional heat equation with a time-dependent coefficient of thermal conductivity is studied. Methods. The article is used Cauchy problems for the heat equation, resolvent methods for Volterra type integral equation and contraction mapping prinsiple.