Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Comparison principle for some nonlocal problems

Author: Keng Deng
Journal: Quart. Appl. Math. 50 (1992), 517-522
MSC: Primary 35K60; Secondary 35B05
DOI: https://doi.org/10.1090/qam/1178431
MathSciNet review: MR1178431
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Abstract: In this paper, for the parabolic equation $ {u_t} = \Delta u + g\left( {x, u} \right), \left( {x, t} \right) \in \\ \Omega \times \left( {0, T} \right)$, with nonlocal boundary conditions $ u\left\vert {_{\partial \Omega }} \right. = \int_{\Omega } f\left( {x, y} \right)u\left( {y, t} \right)dy$, we establish the comparison theorem and local existence of the solution. We also discuss its long time behavior.

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DOI: https://doi.org/10.1090/qam/1178431
Article copyright: © Copyright 1992 American Mathematical Society

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