Nonlinear stability of diffusive contact wave for a chemotaxis model
The author considered the following initial value problem \begin{align*} &v_t+u_x=0,&& x\in \mathbb{R},t>0 \\ &u_t+(uv)_x=u_{xx}+ru(1-u),&& x\in \mathbb{R}, t>0, \\ &(v,u)(x,0)=(v_0,u_0)(x),&& x\in \mathbb{R}. \end{align*} The author studied Cauchy problem when the Cauchy data are near a diffusive contact wave, established global existence of solution and studied time asymptotic behavior of the solution. The author also obtained nonlinear stability of the diffusive contact wave. The result shows a significant difference when comparing the above model to Euler equations with damping.
scientific article; zbMATH DE number 7436214
scientific article