论文标题
时间周期域的反应扩散问题
Reaction-Diffusion Problems on Time-Periodic Domains
论文作者
论文摘要
在零dirichlet边界条件的有界的，时间周期的域上研究了反应扩散方程。长期行为证明取决于转化的周期性羟基问题的主要周期性特征值。我们证明了该特征值的上限和下限在域上的一系列不同假设下，并将其应用于示例。主特征值被视为频率的函数，并在小频率限制中给出了其行为的结果。还证明了相对于频率的单调性能。然后在周期性域上研究了一类可单线非线性的反应扩散问题，我们证明收敛到零或唯一的阳性周期性解决方案。
Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem. We prove upper and lower bounds on this eigenvalue under a range of different assumptions on the domain, and apply them to examples. The principal eigenvalue is considered as a function of the frequency, and results are given regarding its behaviour in the small and large frequency limits. A monotonicity property with respect to frequency is also proven. A reaction-diffusion problem with a class of monostable nonlinearity is then studied on a periodic domain, and we prove convergence to either zero or a unique positive periodic solution.
