论文标题
非局部双重反应扩散方程的渐近行为
Asymptotic behavior of nonlocal bistable reaction-diffusion equations
论文作者
论文摘要
在本文中，我们研究了从紧凑的初始条件开始的非局部双重反应扩散方程溶液的渐近行为。根据非线性，相互作用内核和扩散系数之间的关系，我们表明解决方案可以：传播，灭绝或保持固定。我们尤其关注后一种制度，通过彻底研究该问题的不连续的基态解决方案，以作为案例研究的特定相互作用内核。我们还对问题进行了详细的数值分析。
In this paper, we study the asymptotic behavior of the solutions of nonlocal bistable reaction-diffusion equations starting from compactly supported initial conditions. Depending on the relationship between the nonlinearity, the interaction kernel and the diffusion coefficient, we show that the solutions can either: propagate, go extinct or remain pinned. We especially focus on the latter regime where solutions are pinned by thoroughly studying discontinuous ground state solutions of the problem for a specific interaction kernel serving as a case study. We also present a detailed numerical analysis of the problem.
