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Volume 24, Issue 4
Analysis of a Free Boundary Problem Modeling Multi-layer Tumor Growth in Presence of Inhibitor

Xiumei Hou

DOI: 10.4208/jpde.v24.n4.2

J. Part. Diff. Eq., 24 (2011), pp. 297-312.

Published online: 2011-11

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  • Abstract

In this paper we study well-posedness and asymptotic behavior of solution of a free boundary problem modeling the growth of multi-layer tumors under the action of an external inhibitor. We first prove that this problem is locally well-posed in little H“older spaces. Next we investigate asymptotic behavior of the solution. By making delicate analysis of spectrum of the linearization of the stationary free boundary problemand using the linearized stability theorem, we prove that if the surface tension coefficient γ is larger than γ^∗ > 0 the flat stationary solution is asymptotically stable provided that the constant c representing the ratio between the nutrient diffusion time and the tumor-cell doubling time is sufficient small.

  • Keywords

Free boundary problem multi-layer tumor inhibitor well-posedness

  • AMS Subject Headings

35B35 35R35 76D27

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-24-297, author = {Xiumei Hou }, title = {Analysis of a Free Boundary Problem Modeling Multi-layer Tumor Growth in Presence of Inhibitor}, journal = {Journal of Partial Differential Equations}, year = {2011}, volume = {24}, number = {4}, pages = {297--312}, abstract = {

In this paper we study well-posedness and asymptotic behavior of solution of a free boundary problem modeling the growth of multi-layer tumors under the action of an external inhibitor. We first prove that this problem is locally well-posed in little H“older spaces. Next we investigate asymptotic behavior of the solution. By making delicate analysis of spectrum of the linearization of the stationary free boundary problemand using the linearized stability theorem, we prove that if the surface tension coefficient γ is larger than γ^∗ > 0 the flat stationary solution is asymptotically stable provided that the constant c representing the ratio between the nutrient diffusion time and the tumor-cell doubling time is sufficient small.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v24.n4.2}, url = {http://global-sci.org/intro/article_detail/jpde/5212.html} }
TY - JOUR T1 - Analysis of a Free Boundary Problem Modeling Multi-layer Tumor Growth in Presence of Inhibitor AU - Xiumei Hou JO - Journal of Partial Differential Equations VL - 4 SP - 297 EP - 312 PY - 2011 DA - 2011/11 SN - 24 DO - http://doi.org/10.4208/jpde.v24.n4.2 UR - https://global-sci.org/intro/article_detail/jpde/5212.html KW - Free boundary problem KW - multi-layer tumor KW - inhibitor KW - well-posedness AB -

In this paper we study well-posedness and asymptotic behavior of solution of a free boundary problem modeling the growth of multi-layer tumors under the action of an external inhibitor. We first prove that this problem is locally well-posed in little H“older spaces. Next we investigate asymptotic behavior of the solution. By making delicate analysis of spectrum of the linearization of the stationary free boundary problemand using the linearized stability theorem, we prove that if the surface tension coefficient γ is larger than γ^∗ > 0 the flat stationary solution is asymptotically stable provided that the constant c representing the ratio between the nutrient diffusion time and the tumor-cell doubling time is sufficient small.

Xiumei Hou . (2011). Analysis of a Free Boundary Problem Modeling Multi-layer Tumor Growth in Presence of Inhibitor. Journal of Partial Differential Equations. 24 (4). 297-312. doi:10.4208/jpde.v24.n4.2
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