A Free Boundary Problem for an Elliptic-Parabolic System: Application to a Model of Tumor Growth

A Free Boundary Problem for an Elliptic-Parabolic System: Application to a Model of Tumor Growth

In this article, we study a free boundary problem for a system of two partial differential equations, one parabolic and other elliptic. The system models the growth of a tumor with arbitrary initial shape. We establish the existence and uniqueness of a solution for some time interval. In the special...

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Veröffentlicht in:Communications in partial differential equations 2003-01, Vol.28 (3-4), p.517-560
Hauptverfasser: Bazaliy, Borys V., Friedman, Avner
Format: Artikel
Sprache:eng
Schlagworte:
Elliptic variational inequality
Elliptic-parabolic system
Free boundary problem
Tumor growth
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Zusammenfassung:In this article, we study a free boundary problem for a system of two partial differential equations, one parabolic and other elliptic. The system models the growth of a tumor with arbitrary initial shape. We establish the existence and uniqueness of a solution for some time interval. In the special case where we only have the elliptic equation, the problem coincides with the Hele-Shaw problem.
ISSN:0360-5302
1532-4133
DOI:10.1081/PDE-120020486