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Nonlinear Phenomena in Evolutionary Partial Differential Equations
15:30 - 17:30, May 26, 2020 (Tuesday)
R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Generalization of Propagation Speed with Variation Structure in Reaction-diffusion System of Gradient Type
Yi-Yun Lee (National Taiwan University)


We study the following initial value problem :
,      (1)
where , is a bounded domain with smooth boundary, is in , with either Neumann or Dirichlet boundary conditions. This problem describes a reaction-diffusion system with equal diffusion coefficients defined inside an n-dimensional cylinder .
We assume that , so is a trivial solution of above equations.
If there exists a function such that
then we called it reaction-diffusion of gradient type.
Traveling solutions are important in these systems and a lot of researchers study related topics, including existence and stability of traveling wave solutions in vary domains and traveling wave solutions selections.
Furthermore, following from ideas in Muratov's study [1], we introduce "wave-like" solutions and propagation speed of such solutions by variation structures, and we proved that propagation speed of wave-like solutions is monotone increasing.
[1] CB Muratov. A global variational structure and propagation of disturbances in reaction-diffusion systems of gradient type. Discrete & Continuous Dynamical Systems-B, 4(4):867, 2004.


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