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Local existence and uniqueness of solutions to approximate systems of 1D tumor invasion model

Artykuł
Czasopismo : NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS   Tom: 11, Zeszyt: 5, Strony: 3555-3566
Ito Akio , Maria Gokieli [1] , Marek Niezgódka [1] , Zuzanna Szymańska [1]
2010 angielski
Identyfikatory
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Słowa kluczowe
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Abstrakty ( angielski )
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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.
Bibliografia
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  7. Horstmann, D., "From 1970 until present: The Keller–Segel model in chemotaxis and its consequences", Jahresber. Deutsch. Math. Verein., vol. 105, 2003, p.103-165
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  9. Fontelos, M.A.& Friedman, A.& Hu, B., "Mathematical analysis of a model for the initiation of angiogenesis", SIAM J. Math. Anal., vol. 33, 2002, p.1330-1355
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  11. Corrias, L.& Perthame, B.& Zaag, H., "Global solutions of some chemotaxis and angiogenesis systems in high space dimensions", Milan J. Math., vol. 72, 2004, p.1-28
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