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Mathematical Biosciences and Engineering

2015, Volume 12, Issue 6: 1173-1187. doi: 10.3934/mbe.2015.12.1173
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Mathematical model and its fast numerical method for the tumor growth

  • 1.
    Institute of Mathematical Sciences, Ewha Womans University, Seoul 120-750
  • 2.
    Department of Mathematics, Konkuk University, Seoul 143-701
  • 3.
    Department of Mathematics, Korea University, Seoul 136-713
  • Received: 01 October 2014 Accepted: 29 June 2018 Published: 01 August 2015

  • MSC : Primary: 65M06; Secondary: 92B05.

  • 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-orderAllen--Cahn equation with a space--time dependent Lagrange multiplier instead of using thefourth-order Cahn--Hilliard equation in the original model. To numerically solve the new model, weapply a recently developed hybrid numerical method. We perform various numerical experiments. Thecomputational results demonstrate that the new model is not only fast but also has a good featuresuch as distributing excess mass from the inside of tumor to its boundary regions.

    Citation: Hyun Geun Lee, Yangjin Kim, Junseok Kim. Mathematical model and its fast numerical method for the tumor growth[J]. Mathematical Biosciences and Engineering, 2015, 12(6): 1173-1187. doi: 10.3934/mbe.2015.12.1173

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  • 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-orderAllen--Cahn equation with a space--time dependent Lagrange multiplier instead of using thefourth-order Cahn--Hilliard equation in the original model. To numerically solve the new model, weapply a recently developed hybrid numerical method. We perform various numerical experiments. Thecomputational results demonstrate that the new model is not only fast but also has a good featuresuch as distributing excess mass from the inside of tumor to its boundary regions.


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