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Analysis of a mixture model of tumor growth

Published online by Cambridge University Press:  07 May 2013

JOHN LOWENGRUB ,
EDRISS TITI  and
KUN ZHAO
JOHN LOWENGRUB
Affiliation:
Departments of Mathematics and Biomedical Engineering, University of California, Irvine, CA 92697-3875, USA email: lowengrb@math.uci.edu
EDRISS TITI
Affiliation:
Departments of Mathematics and Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3875, USA; Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel email: etiti@math.uci.edu
KUN ZHAO
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118-5665, USA email: kzhao@tulane.edu
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Abstract

We study an initial-boundary value problem for a coupled Cahn–Hilliard–Hele–Shaw system that models tumour growth. For large initial data with finite energy, we prove global (local resp.) existence, uniqueness, higher order spatial regularity and the Gevrey spatial regularity of strong solutions to the initial-boundary value problem in two dimensions (three dimensions resp.). Asymptotically in time, we show that the solution converges to a constant state exponentially fast as time tends to infinity under certain assumptions.

Keywords

Cahn–Hilliard–Hele–Shaw equationGlobal existence and uniquenessRegularityGevrey class regularityLong-time asymptotic behaviour
Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 5 , October 2013 , pp. 691 - 734
Copyright
Copyright © Cambridge University Press 2013 

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