一类混合型趋化模型的黎曼问题

Riemann Problem for a Class of Mixed-type Chemotaxis Models

该文研究了一类双曲椭圆混合型趋化模型的黎曼问题.该方程组在v-轴上是线性退化的.我们在相平面上得到了初始左右状态在不同区域时黎曼解存在的可解域.特别地,当左状态在第二象限,右状态在第一象限时,该混合型方程组的初值问题都是黎曼可解的.

In this paper,we consider the Riemann problem for a system arising in chemotaxis.The system is of mixed type and transitions from a hyperbolic to an elliptic region.It is linearly degenerated along the v-axis.We obtain a solvable domain in the phase plane for the existence of Riemann solutions when the initial left and right states are in different regions.In particular,when the left state is fixed in the second quadrant and any right state is in the first quadrant,the initial value problem of this mixed-type system is Riemann solvable.