Publications [#359347] of Jian-Guo Liu

Papers Published

1. Liu, JG; Xu, X, Existence and incompressible limit of a tissue growth model with autophagy, SIAM Journal on Mathematical Analysis, vol. 53 no. 5 (January, 2021), pp. 5215-5242 [doi] [reputed journal]
   (last updated on 2025/05/01)

   Abstract:
   In this paper we study a cross-diffusion system whose coefficient matrix is non-symmetric and degenerate. The system arises in the study of tissue growth with autophagy. The existence of a weak solution is established. We also investigate the limiting behavior of solutions as the pressure gets stiff. The so-called incompressible limit is a free boundary problem of Hele-Shaw type. Our key new discovery is that the usual energy estimate still holds as long as the time variable stays away from 0.