Title: Convergence rate for the incompressible limit of nonlinear diffusion-advection equations Show Chinese title

Title: 非线性扩散-对流方程的不可压缩极限的收敛速率

Abstract: The incompressible limit of nonlinear diffusion equations of porous medium type has attracted a lot of attention in recent years, due to its ability to link the weak formulation of cell-population models to free boundary problems of Hele-Shaw type. Although vast literature is available on this singular limit, little is known on the convergence rate of the solutions. In this work, we compute the convergence rate in a negative Sobolev norm and, upon interpolating with BV-uniform bounds, we deduce a convergence rate in appropriate Lebesgue spaces. Show Chinese abstract

Abstract: 不可压缩极限的非线性扩散方程的多孔介质类型近年来引起了广泛关注，因为它能够将细胞种群模型的弱形式与Hele-Shaw类型的自由边界问题联系起来。 尽管关于这一奇异极限有大量的文献，但对解的收敛速率了解甚少。 在本工作中，我们计算了负Sobolev范数中的收敛速率，并通过与BV一致界进行插值，推导出适当Lebesgue空间中的收敛速率。