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On some class of problems with nonlocal source and boundary flux


Chipot, M; Rougirel, A (2001). On some class of problems with nonlocal source and boundary flux. Advances in Differential Equations, 6(9):1025-1048.

Abstract

In this paper we study an nonlocal, semilinear, parabolic problem. The existence and uniqueness of a maximal solution is proved for bounded domains, in arbitrary dimensions, using the Schauder fixed-point theorem. In the one-dimensional case, we give a result of positivity and a comparison principle for the integral of the solution. The proofs are based on the decomposition of the solutions in an appropriate spectral basis.

Abstract

In this paper we study an nonlocal, semilinear, parabolic problem. The existence and uniqueness of a maximal solution is proved for bounded domains, in arbitrary dimensions, using the Schauder fixed-point theorem. In the one-dimensional case, we give a result of positivity and a comparison principle for the integral of the solution. The proofs are based on the decomposition of the solutions in an appropriate spectral basis.

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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
Uncontrolled Keywords:nonlocal problem; semilinear parabolic problem; maximal solution; Schauder fixed point theorem
Language:English
Date:2001
Deposited On:28 Jun 2010 14:06
Last Modified:06 Dec 2017 20:52
Publisher:Khayyam
ISSN:1079-9389
Free access at:Official URL. An embargo period may apply.
Official URL:http://www.aftabi.com/ADE/ADE-V6-Figs/ade-34.gif
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1852627
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1010.35055

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