A Free Boundary Problem for an Elliptic–Parabolic System: Application to a Model of Tumor Growth
Borys V. BazaliyInstitute of Applied Mathematics and Mechanics , National Academy of Sciences , Donetsk, UkraineAvner FriedmanUniversity of Minnesota, Department of Mathematics , Minneapolis, Minnesota
2003en
ABI
Abstract
Abstract 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.
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Cited by 40 references