Advances in Differential Equations

On some class of problems with nonlocal source and boundary flux

M. Chipot and A. Rougirel

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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.

Article information

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

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1357140403

Mathematical Reviews number (MathSciNet)
MR1852627

Zentralblatt MATH identifier
1010.35055

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

Citation

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.


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