Publications [#366656] of Jian-Guo Liu

Papers Published

1. Liu, JG; Tang, M; Wang, L; Zhou, Z, Toward understanding the boundary propagation speeds in tumor growth models, SIAM Journal on Applied Mathematics, vol. 81 no. 3 (January, 2021), pp. 1052-1076 [doi]
   (last updated on 2025/02/21)

   Abstract:
   At the continuous level, we consider two types of tumor growth models: the cell density model, based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations, and the free boundary model, as the incompressible limit of the former, is more tractable when investigating the boundary propagation. In this work, we aim to investigate the boundary propagation speeds in those models based on asymptotic analysis of the free boundary model and efficient numerical simulations of the cell density model. We derive, for the first time, some analytical solutions for the free boundary model with pressure jumps across the tumor boundary in multidimensions with finite tumor sizes. We further show that in the large radius limit, the analytical solutions to the free boundary model in one and multiple spatial dimensions converge to traveling wave solutions. The convergence rate in the propagation speeds are algebraic in multidimensions as opposed to the exponential convergence in one dimension. We also propose an accurate front capturing numerical scheme for the cell density model, and extensive numerical tests are provided to illustrate the analytical findings.