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NCTS Seminar on Mathematical Biology
 
15:00 - 15:50, November 1, 2019 (Friday)
Lecture Room B, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館 4樓B演講室)
Concentration and Singular Waves in a Nonlocal Reaction-diffusion Equation
Quentin Griette (University of Bordeaux)

Abstract:

I consider a reaction-diffusion equation modelling the propagation of a species that possesses a continuum of phenotypic traits. The spatial dynamics of the individuals is modelled by a diffusion process, and the population undergoes a reproduction-mutation-competition dynamics at each spatial point, which is modelled by a nonlocal operator acting on the bounded domain representing the phenotypic space. Under some conditions on the fitness function, the mutation rate and the dimensionality of the domain, a concentration phenomenon is known to happen for the linearized equation, meaning that a singular measure part exists in the principal eigenfunction. I will discuss the validity of this phenomenon for the full (nonlinear) equation, with a particular attention to homogeneous stationary states and traveling waves. In particular, I will talk about the techniques used to construct weak (possibly singular) traveling waves.



 

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