Rothe method for a mixed problem with an integral condition for the two‐dimensional diffusion equation

Nabil Merazga and Abdelfatah Bouziani

Abstract and Applied Analysis, 2003, vol. 2003, issue 16, 899-922

Abstract: This paper deals with an initial boundary value problem with an integral condition for the two‐dimensional diffusion equation. Thanks to an appropriate transformation, the study of the given problem is reduced to that of a one‐dimensional problem. Existence, uniqueness, and continuous dependence upon data of a weak solution of this latter are proved by means of the Rothe method. Besides, convergence and an error estimate for a semidiscrete approximation are obtained.

Date: 2003
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https://doi.org/10.1155/S1085337503305019

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2003:y:2003:i:16:p:899-922

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