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On a class of integro-differential problems


Chipot, M; Guesmia, S (2010). On a class of integro-differential problems. Communications on Pure and Applied Analysis, 9(5):1249-1262.

Abstract

The paper is concerned with the existence of solutions to an integro-differential problem arising in the neutron transport theory. By an anisotropic singular perturbations method we show that solutions of such a problem exist and are close to those of some nonlocal elliptic problem. The existence of the solutions of the nonlocal elliptic problem with bounded data is ensured by the Schauder fixed point theorem. Then an asymptotic method is applied in the general case. The limits of the solutions of the nonlocal elliptic problems are solutions of our integro-differential problem.

Abstract

The paper is concerned with the existence of solutions to an integro-differential problem arising in the neutron transport theory. By an anisotropic singular perturbations method we show that solutions of such a problem exist and are close to those of some nonlocal elliptic problem. The existence of the solutions of the nonlocal elliptic problem with bounded data is ensured by the Schauder fixed point theorem. Then an asymptotic method is applied in the general case. The limits of the solutions of the nonlocal elliptic problems are solutions of our integro-differential problem.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:September 2010
Deposited On:15 Nov 2010 11:55
Last Modified:05 Apr 2016 14:16
Publisher:American Institute of Mathematical Sciences
ISSN:1534-0392
Publisher DOI:https://doi.org/10.3934/cpaa.2010.9.1249
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2645994

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