title: Mathematical model and its fast numerical method for the tumor growth.
abstract: In this paper, we reformulate the diffuse interface model of the tumor growth (S.M. Wise et al., Three-dimensional multispecies nonlinear tumor growth-I: model and numerical method, J. Theor. Biol. 253 (2008) 524--543). In the new proposed model, we use the conservative second-order Allen--Cahn equation with a space--time dependent Lagrange multiplier instead of using the fourth-order Cahn--Hilliard equation in the original model. To numerically solve the new model, we apply a recently developed hybrid numerical method. We perform various numerical experiments. The computational results demonstrate that the new model is not only fast but also has a good feature such as distributing excess mass from the inside of tumor to its boundary regions.
authors.affiliation: Institute of Mathematical Sciences, Ewha Womans University, Seoul 120-750, South Korea. email:leeh@korea.ac.kr.
authors.forename: Hyun Geun
authors.initials: HG
authors.lastname: Lee
authors.forename: Yangjin
authors.initials: Y
authors.lastname: Kim
authors.forename: Junseok
authors.initials: J
authors.lastname: Kim
mesh_terms: D000465:Algorithms; D049109:Cell Proliferation; D003198:Computer Simulation; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology*; D017711:Nonlinear Dynamics