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, 1-24

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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:639847

DOI: 10.1155/S1085337503305019

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