Local existence and uniqueness of solutions to one-dimensional tumor invasion model

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Authors
Ito, Akio
Gokieli, Maria
Niezgódka, Marek
Szymańska, Zuzanna
Date
2010
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
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Abstract
In the present paper, we propose a modified tumor invasion model which was originally proposed in Chaplain and Anderson (2003) [1]. And we show the local existence and uniqueness of solutions to approximate systems of the 1D modified tumor invasion model. Especially, we introduce a new function and show that our system is equivalent to the nonlinear second-order PDE, which should be reformulated by the new function. Roughly speaking, our system can be rewritten into only one second-order PDE and this fact is quite essential to show the local existence of solutions to the approximate systems.
Description
Keywords
Tumor invasion    Haptotaxis-degenerate system    Nonlinear second-order PDE
Citation
A. Ito, M. Gokieli, M. Niezgódka and Z. SZymańska, Local existence and uniqueness of solutions to one-dimensional tumor invasion model, Nonlinear Analysis B - RWA, Volume 11, Issue 5, 2010, pp. 3555-3566
URI
http://depot.ceon.pl/handle/123456789/69
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Artykuły ICM / ICM Articles