论文标题
半线性抛物线和椭圆方程的单调方法
Monotone methods for semilinear parabolic and elliptic equations on graphs
论文作者
论文摘要
本文致力于研究解决图laplacian抛物面问题的解决方案的灭绝和传播特性，其中包括KPP类型或Allen-Cahn类型强迫术语在图上。为此，我们建立了（强）最大原理以及图形上抛物线和椭圆形问题的上和下部解决方案方法。通过构建合适的上和下溶液来研究平衡溶液的稳定性。此外，我们提供了一个示例和数值实验，以证明我们的主要结果之一。
This paper is devoted to investigate the extinction and propagation properties of solutions to the graph Laplacian parabolic problems with Kpp type or Allen-Cahn type forcing terms on graphs. To this end, we establish the (strong) maximum principle and the upper and lower solutions method for parabolic and elliptic problems on graphs. The stability of equilibrium solutions is studied by constructing suitable upper and lower solutions. Moreover, we give an example and numerical experiments to demonstrate one of our main results.
