Transmutation Operator Method for Solving Heat Conduction Problem

The transmutation operator method is extended to the case of functions two variables. flattens function, i.e. replaces a function with discontinuous partial derivatives on coordinate axes by continuously differentiable function. work reveal properties operator, and prove commutativity Laplace operator. It was found that Cauchy problem for equation internal conjugations in an unbounded domain can be replaced model twodimensional equation. As result, new analytical solving initial-boundary value problems two-dimensional heat has been developed. factorization established as product one-dimensional operators. form establishing isomorphism mathematical models conduction media different physical characteristics descrfibed.