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

Т. Ш. Кальменов | Zendy; Niyaz Tokmagambetov | Zendy

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

Author(s) -

Т. Ш. Кальменов,

Niyaz Tokmagambetov

Publication year - 2013

Publication title -

isrn mathematical analysis

Language(s) - English

Resource type - Journals

eISSN - 2090-4665

pISSN - 2090-4657

DOI - 10.1155/2013/640985

Subject(s) - tikhonov regularization , cauchy problem , mathematics , heat equation , a priori and a posteriori , cauchy distribution , initial value problem , cauchy's convergence test , integral equation , mathematical analysis , fourier transform , cauchy boundary condition , inverse problem , boundary value problem , philosophy , epistemology , free boundary problem

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.

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