论文标题
非局部反应扩散方程的阈值解
Threshold solutions for nonlocal reaction diffusion equations
论文作者
论文摘要
我们研究了1D空间结构域中具有双重非线性的非局部反应扩散方程的Cauchy问题，并研究了溶液的渐近行为，其单调增加和紧凑的初始数据具有单参数家族。我们表明，对于参数的小值，相应的溶液衰减至0，而对于大值，相关的解决方案在紧凑型上均匀地收敛至1。此外，我们证明了从灭绝（收敛到0）到繁殖（收敛到1）的过渡很清晰。提供数值结果以验证理论结果。
We study the Cauchy problem for nonlocal reaction diffusion equations with bistable nonlinearity in 1D spatial domain and investigate the asymptotic behaviors of solutions with a one-parameter family of monotonically increasing and compactly supported initial data. We show that for small values of the parameter the corresponding solutions decay to 0, while for large values the related solutions converge to 1 uniformly on compacts. Moreover, we prove that the transition from extinction (converging to 0) to propagation (converging to 1) is sharp. Numerical results are provided to verify the theoretical results.
