Advances in Differential Equations

On some class of problems with nonlocal source and boundary flux

M. Chipot and A. Rougirel

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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.

Article information

Adv. Differential Equations, Volume 6, Number 9 (2001), 1025-1048.

First available in Project Euclid: 2 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35A15: Variational methods 35K20: Initial-boundary value problems for second-order parabolic equations


Chipot, M.; Rougirel, A. On some class of problems with nonlocal source and boundary flux. Adv. Differential Equations 6 (2001), no. 9, 1025--1048.

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