The existence of the weak solutions and the traveling waves to the hyperbolic and parabolic-hyperbolic Keller-Segel equations in chemotaxis.


Meng-Kai Hong

09:10:00 - 10:00:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, we consider the general hyperbolic Keller-Segel equations in chemotaxis, which can be written as the hyperbolic systems of balance laws. We establish the global existence of the weak solutions to the Riemann and Cauchy problems by the generalized Lax method and the modified Glimm scheme. To the parabolic-hyperbolic K-S equations, we study the existence and the behavior of the traveling wave solutions by the technique of geometric singular perturbations. This is the joint work with J. S. Guo of Tamkang University and Y. S. Chen of National Central University

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