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Nonlinear Phenomena in Evolutionary Partial Differential Equations
15:30 - 17:30, September 29, 2020 (Tuesday)
R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Generalization of Propagation Speed in Reaction-diffusion Systems 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 system of gradient type.
Traveling solutions play an important role in such systems and a lot of researchers study related topics, including existence and stability of traveling wave solutions in vary domains and corresponding wave speed.
Furthermore, following from ideas in Muratov's study \cite{muratov2004global}, we introduce a wide class of solutions, called "wave-like" solutions, and  show that well-defined instantaneous propagation speed for such solutions monotone converges to a limit at long time. Furthermore, with more assumptions, we could show it converges to traveling wave solution with such speed.


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