Asymptotic behavior of solutions of a free boundary problem modeling the growth of tumors with fluid-like tissue under the action of inhibitors (Q2847034)
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scientific article; zbMATH DE number 6204712
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic behavior of solutions of a free boundary problem modeling the growth of tumors with fluid-like tissue under the action of inhibitors |
scientific article; zbMATH DE number 6204712 |
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Asymptotic behavior of solutions of a free boundary problem modeling the growth of tumors with fluid-like tissue under the action of inhibitors (English)
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4 September 2013
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free boundary problem
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tumor growth
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Stokes equation
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radial stationary solution
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asymptotic stability
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This paper deals with a free boundary problem modeling the growth of tumors with fluid-like tissue under the action of inhibitors. The model includes two elliptic equations describing the concentration of nutrients and inhibitors, respectively, and a Stokes equation for the fluid velocity and internal pressure. The authors convert the problem with free boundary into an initial-boundary value problem on a fixed domain. Then, the Cauchy problem of an abstract differential equation in a Banach space is investigated. The main result is the stability and the instability of stationary solutions depending on the data of the problem.
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