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2001 On some class of problems with nonlocal source and boundary flux
M. Chipot, A. Rougirel
Adv. Differential Equations 6(9): 1025-1048 (2001). DOI: 10.57262/ade/1357140403

Abstract

In this paper we study a 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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M. Chipot. A. Rougirel. "On some class of problems with nonlocal source and boundary flux." Adv. Differential Equations 6 (9) 1025 - 1048, 2001. https://doi.org/10.57262/ade/1357140403

Information

Published: 2001
First available in Project Euclid: 2 January 2013

zbMATH: 1010.35055
MathSciNet: MR1852627
Digital Object Identifier: 10.57262/ade/1357140403

Subjects:
Primary: 35K55
Secondary: 35A15 , 35K20

Rights: Copyright © 2001 Khayyam Publishing, Inc.

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Vol.6 • No. 9 • 2001
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