4 citations · 8 across the 5 of their papers we have counts for
6 papers
Tumor Growth with Nutrients: Regularity and Stability
Matt Jacobs, Inwon Kim, Jiajun Tong
In this paper we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the contact inhibition among the tumor cells. We show that when the nu…
Darcy's Law with a Source term
Matt Jacobs, Inwon Kim, Jiajun Tong
We introduce a novel variant of the JKO scheme to approximate Darcy's law with a pressure dependent source term. By introducing a new variable that implicitly controls the source t…
The -contraction principle in optimal transport
Matt Jacobs, Inwon Kim, Jiajun Tong
In this work, we use the JKO scheme to approximate a general class of diffusion problems generated by Darcy's law. Although the scheme is now classical, if the energy density is sp…
Interface Dynamics in a Two-phase Tumor Growth Model
Inwon Kim, Jiajun Tong
We study a tumor growth model in two space dimensions, where proliferation of the tumor cells leads to expansion of the tumor domain and migration of surrounding normal tissues int…
Regularized Stokes Immersed Boundary Problems in Two Dimensions: Well-posedness, Singular Limit, and Error Estimates
Jiajun Tong
Inspired by the numerical immersed boundary method, we introduce regularized Stokes immersed boundary problems in two dimensions to describe regularized motion of a 1-D closed elas…
Directed migration of microscale swimmers by an array of shaped obstacles: modeling and shape optimization
Jiajun Tong, Michael J. Shelley
Achieving macroscopic directed migration of microscale swimmers in a fluid is an important step towards utilizing their autonomous motion. It has been experimentally shown that dir…