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

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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.

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Uncontrolled Keywords:nonlocal problem; semilinear parabolic problem; maximal solution; Schauder fixed point theorem
Deposited On:28 Jun 2010 14:06
Last Modified:23 Nov 2012 16:29
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
Citations:Google Scholar™
Scopus®. Citation Count: 2

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