Advances in Differential Equations
- Adv. Differential Equations
- Volume 6, Number 9 (2001), 1025-1048.
On some class of problems with nonlocal source and boundary flux
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.
Adv. Differential Equations Volume 6, Number 9 (2001), 1025-1048.
First available in Project Euclid: 2 January 2013
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Chipot, M.; Rougirel, A. On some class of problems with nonlocal source and boundary flux. Adv. Differential Equations 6 (2001), no. 9, 1025--1048. https://projecteuclid.org/euclid.ade/1357140403.