Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (2): 305-319.

• Articles • Previous Articles     Next Articles

Existence and Uniqueness of Global Solutions for a Free Boundary Problem Modeling the Growth of Tumors under the Action of Drugs

WU Jun-De, CUI Shang-Bin   

  1. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275
  • Received:2008-08-26 Revised:2009-10-18 Online:2010-04-25 Published:2010-04-25
  • Supported by:

    国家自然科学基金(10771223)资助.

Abstract:

In this paper a mathematical model for the effect of drugs in the growth of tumors is studied. This model is a modification of the Jackson model by dividing tumor cells into three classes: proliferating cells, dormant cells and dead cells. The model is a free boundary problem of a system of partial differential equations comprising a second-order nonlinear parabolic equation and two first-order nonlinear partial differential equations. By applying the Lp theory of parabolic equations, the characteristic method for first-order partial differential equations, and the Banach fixed point theorem, existence and uniqueness of the global classic solution are established.

Key words: Tumor growth, Free boundary problem, Global solution

CLC Number: 

  • 34B15
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