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September  2010, 9(5): 1249-1262. doi: 10.3934/cpaa.2010.9.1249

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, Switzerland

Received  September 2009 Revised  October 2009 Published  May 2010

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.
Keywords: anisotropic singular perturbations, Integro-partial differential equations, asymptotic behaviour, elliptic problems., Schauder fixed point theorem, neutron transport.
Mathematics Subject Classification: Primary: 35B25, 35B40, 45K05; Secondary: 35J25, 82D7.
Citation: Michel Chipot, Senoussi Guesmia. On a class of integro-differential problems. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1249-1262. doi: 10.3934/cpaa.2010.9.1249
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