Uniqueness of the weak solution to a cross-diffusion system without volume-filling
Xi Lin
公開日: 2022/3/27
Abstract
We consider a system of parabolic partial differential equations with cross-diffusion phenomenon. Previous results have shown that a weak solution exists to the semiconductor model with electron-hole scattering. In this work, we show that this weak solution exists uniquely. The weak solution of the semiconductor model may not be bounded, and we rely on the structural character of this model to show its uniqueness.