Method of external potential in solution of Cauchy mixed problem for the heat equation (Q2449009)

Summary: Numerous research works are devoted to study Cauchy mixed problem for model heat equations because of its theoretical and practical importance. Among them we can notice monographers [\textit{V. S. Vladimirov}, Equations of mathematical physics (1971; Zbl 0231.35002); \textit{O. A. Ladyzhenskaya} [Boundary value problems of mathematical physics. Moskau: Nauka (1973; Zbl 0284.35001)], and \textit{A. N. Tikhonov} and \textit{A. A. Samarskij} [Equations of mathematical physics. Moscow: Nauka (1972; Zbl 0265.35003)] which demonstrate main research methods, such as Fourier method, integral equations method, and the method of a priori estimates. But at the same time to represent the solution of Cauchy mixed problem in integral form by given and known functions has not been achieved up to now. This paper completes this omission for the one-dimensional heat equation.