论文标题
外部域非局部分散方程的传播现象
Propagation Phenomena for Nonlocal Dispersal Equations in Exterior Domains
论文作者
论文摘要
本文涉及外部域中具有可动或多稳态非线性的非局部分散方程的空间传播。我们获得了整个解决方案的存在和独特性，该解决方案的表现像平面波界，随着时间的流逝，无穷大。特别是，随着整个解决方案出现到内部域，整个溶液的轮廓上的某些干扰会发生。但是由于整个溶液远离内部域，干扰消失了。此外，我们证明该解决方案可以逐渐恢复其平面波轮廓，并继续沿着与时间相同的方向传播，用于正向凸内部域的正无穷大。我们的工作概括了Berestycki等人获得的局部（拉普拉斯）扩散结果。 （2009年）通过使用新的已知liouville结果以及由于Li等人而引起的整个解决方案的Lipschitz连续性来实现非局部扩散设置。 （2010）。
This paper is concerned with the spatial propagation of nonlocal dispersal equations with bistable or multistable nonlinearity in exterior domains. We obtain the existence and uniqueness of an entire solution which behaves like a planar wave front as time goes to negative infinity. In particular, some disturbances on the profile of the entire solution happen as the entire solution comes to the interior domain. But the disturbances disappear as the entire solution is far away from the interior domain. Furthermore, we prove that the solution can gradually recover its planar wave profile and continue to propagate in the same direction as time goes to positive infinity for compact convex interior domain. Our work generalizes the local (Laplace) diffusion results obtained by Berestycki et al. (2009) to the nonlocal dispersal setting by using new known Liouville results and Lipschitz continuity of entire solutions due to Li et al. (2010).
