On a class of integro-differential problems

Pages: 1249 - 1262, Volume 9, Issue 5, September 2010

doi:10.3934/cpaa.2010.9.1249       Abstract        Full Text (170.6K)       Related Articles

Michel Chipot - Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland (email)
Senoussi Guesmia - University of Zürich, Institute of Mathematics, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland (email)

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.

Keywords:  Integro-partial differential equations, anisotropic singular perturbations, asymptotic behaviour, neutron transport, Schauder fixed point theorem, elliptic problems.
Mathematics Subject Classification:  Primary: 35B25, 35B40, 45K05; Secondary: 35J25, 82D75.

Received: September 2009;      Revised: October 2009;      Published: May 2010.