On the solvability of parabolic and hyperbolic problems with a boundary integral conditionReport as inadecuate




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International Journal of Mathematics and Mathematical Sciences - Volume 31 2002, Issue 4, Pages 201-213



Département de Mathématiques, Centre Universitaire Larbi Ben M-hidi-Oum El Bouagui, B.P. 565, 04000, Algeria

Mathematical Division, The Abdus Salam International Centre for Theoretical Physics ICTP, Strada Costiera 11, Trieste 34100, Italy

Received 22 September 2000

Copyright © 2002 Hindawi Publishing Corporation. 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

We prove the existence, uniqueness, and the continuous dependenceof a generalized solution upon the data of certain parabolic andhyperbolic equations with a boundary integral condition. The proofuses a functional analysis method based on a priori estimates established in nonclassical function spaces, and on thedensity of the range of the linear operator associated to theabstract formulation of the studied problem.





Author: Abdelfatah Bouziani

Source: https://www.hindawi.com/



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