The inverse problem for the heat equation with reflection of the argument and with a complex coefficient

Abstract

AbstractThe paper is devoted to finding a solution and restoring the right-hand side of the heat equation with reflection of the argument in the second derivative, with a complex-valued variable coefficient. We prove a theorem on the Riesz basis property for eigenfunctions of the second-order differential operator with involution in the second derivative. We establish the existence and uniqueness of the solution of the studied problems by the method of separation of variables