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FIELD Math:Analysis
DATE January 22 (Wed), 2020
TIME 14:00-16:00
PLACE 1423
SPEAKER Kyudong Choi
HOST Jeong, In-Jee
TITLE Stability of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model
ABSTRACT We consider a simplified chemotaxis model of tumor angiogenesis, described by the Keller-Segel system with logarithmic singular sensitivity with linear consumption rate. The system is known to allow traveling wave solutions (so-called viscous shocks) whose stability has recently received both mathematical and biological interest. In this talk, we study this stability question in two different settings. First, by using a relative entropy functional of the system, which can capture how close a solution at a given time is to a given shock wave in almost L2-sense, the functional is NON-increasing for all time when the shock strength is small enough and it is away from zero-level. Second, stability of PLANAR traveling waves is obtained in two dimensional infinite cylindrical domain by using so-called anti-derivative method with weighted energy estimates allowing zero boundary condition on one end for shocks. If time is permitted, we will introduce stability of Lamb dipole which is a traveling wave of the 2d Euler equations. This talk is based on joint work with M. Kang, Y. Kwon, A. Vasseur and M. Chae, K. Kang, J. Lee and K. Abe.
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