Table of Contents
ISRN Mathematical Analysis
Volume 2013, Article ID 640985, 5 pages
http://dx.doi.org/10.1155/2013/640985
Research Article

Method of External Potential in Solution of Cauchy Mixed Problem for the Heat Equation

Institute of Mathematics and Mathematical Modeling, MES RK, Shevchenko Street, 28, Almaty 050010, Kazakhstan

Received 30 May 2013; Accepted 18 July 2013

Academic Editors: S. Filippas and K. Lurie

Copyright © 2013 T. Sh. Kalmenov and N. E. Tokmagambetov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 Vladimirov (1988), Ladyzhenskaya (1973), and Tikhonov and Samarskyi (1980) 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.