On a class of integro-differential problems

Michel Chipot; Senoussi Guesmia

doi:10.3934/cpaa.2010.9.1249

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2010, Volume 9, Issue 5: 1249-1262. Doi: 10.3934/cpaa.2010.9.1249

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On a class of integro-differential problems

Michel Chipot^1, and
Senoussi Guesmia^2,

1.
Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich
2.
University of Zürich, Institute of Mathematics, Winterthurerstrasse 190, CH-8057 Zürich

Received: August 31, 2009

Revised: September 30, 2009

Published: August 2010

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Abstract

The paper is concerned with the existence of solutions to an integrodifferential 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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Mathematics Subject Classification: Primary: 35B25, 35B40, 45K05; Secondary: 35J25, 82D75.

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