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.
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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of 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.|
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