Jing-Yu Li

Nonlinear stability of composite waves of traveling wave and rarefaction wave for a parabolic-hyperbolic system arising from chemotaxis

We study the nonlinear stability of a composite wave consisting of a traveling wave and a rarefaction wave for a parabolic-hyperbolic system arising from chemotaxis. We prove that if the initial value is a small $H^1$-type perturbation of composite wave, then the system admits a global solution that converges toward th...