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Volume 37, Issue 2
Diffusion with a Discontinuous Potential: A Non-Linear Semigroup Approach

Yong-Jung Kim & Marshall Slemrod

DOI: 10.4208/ata.2021.pr80.01

Anal. Theory Appl., 37 (2021), pp. 178-190.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

This paper studies existence of mild solution to a sharp cut off model for contact driven tumor growth. Analysis is based on application of the Crandall-Liggett theorem for $\omega$-quasi-contractive semigroups on the Banach space $L^1(\Omega)$. Furthermore, numerical computations are provided which compare the sharp cut off model with the tumor growth model of  Perthame, Quirόs, and Vázquez [13].

  • Keywords

Nonlinear semigroups, tumor growth models, Hele-Shaw diffusion.

  • AMS Subject Headings

35Q92, 92C50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-37-178, author = {Kim , Yong-Jung and Slemrod , Marshall}, title = {Diffusion with a Discontinuous Potential: A Non-Linear Semigroup Approach}, journal = {Analysis in Theory and Applications}, year = {2021}, volume = {37}, number = {2}, pages = {178--190}, abstract = {

This paper studies existence of mild solution to a sharp cut off model for contact driven tumor growth. Analysis is based on application of the Crandall-Liggett theorem for $\omega$-quasi-contractive semigroups on the Banach space $L^1(\Omega)$. Furthermore, numerical computations are provided which compare the sharp cut off model with the tumor growth model of  Perthame, Quirόs, and Vázquez [13].

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2021.pr80.01}, url = {http://global-sci.org/intro/article_detail/ata/18770.html} }
TY - JOUR T1 - Diffusion with a Discontinuous Potential: A Non-Linear Semigroup Approach AU - Kim , Yong-Jung AU - Slemrod , Marshall JO - Analysis in Theory and Applications VL - 2 SP - 178 EP - 190 PY - 2021 DA - 2021/04 SN - 37 DO - http://doi.org/10.4208/ata.2021.pr80.01 UR - https://global-sci.org/intro/article_detail/ata/18770.html KW - Nonlinear semigroups, tumor growth models, Hele-Shaw diffusion. AB -

This paper studies existence of mild solution to a sharp cut off model for contact driven tumor growth. Analysis is based on application of the Crandall-Liggett theorem for $\omega$-quasi-contractive semigroups on the Banach space $L^1(\Omega)$. Furthermore, numerical computations are provided which compare the sharp cut off model with the tumor growth model of  Perthame, Quirόs, and Vázquez [13].

Kim , Yong-Jung and Slemrod , Marshall. (2021). Diffusion with a Discontinuous Potential: A Non-Linear Semigroup Approach. Analysis in Theory and Applications. 37 (2). 178-190. doi:10.4208/ata.2021.pr80.01
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