Comparison principle for some nonlocal problems

作者：Keng Deng · 发表于：Quarterly of Applied Mathematics · 年份：1992 · DOI：10.1090/qam/1178431 · 被引用次数：78 · 研究领域：Differential Equations and Boundary Problems、Nonlinear Partial Differential Equations、Differential Equations and Numerical Methods

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.