Comparison principle for some nonlocal problems
- 1 January 1992
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 50 (3) , 517-522
- https://doi.org/10.1090/qam/1178431
Abstract
In this paper, for the parabolic equation u t = Δ u + g ( x , u ) , ( x , t ) ∈ Ω × ( 0 , T ) {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 | ∂ Ω = ∫ Ω f ( x , y ) u ( y , t ) d y u\left | {_{\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.Keywords
This publication has 10 references indexed in Scilit:
- Behavior of Solutions of Burgers′ Equation with Nonlocal Boundary ConditionsJournal of Differential Equations, 1994
- Strong Maximum and Minimum Principles for Parabolic Problems with Non‐local InequalitiesZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1990
- Explicity resolvable equations with functional non-linearitiesMathematical Methods in the Applied Sciences, 1988
- Nonlinear instability for a modified form of Burgers' equationNumerical Methods for Partial Differential Equations, 1987
- Remarks on a paper by W. A. Day on a maximum principle under nonlocal boundary conditionsQuarterly of Applied Mathematics, 1987
- Monotonic decay of solutions of parabolic equations with nonlocal boundary conditionsQuarterly of Applied Mathematics, 1986
- On non-local problems for parabolic equationsNagoya Mathematical Journal, 1984
- A decreasing property of solutions of parabolic equations with applications to thermoelasticityQuarterly of Applied Mathematics, 1983
- Extensions of a property of the heat equation to linear thermoelasticity and other theoriesQuarterly of Applied Mathematics, 1982
- Partial Differential Equations of Parabolio Type. By Avner Friedman. 1964. (Prentice-Hall)The Mathematical Gazette, 1967