Departmental Bulletin Paper Asymptotic Behaviors of Solutions to One-dimensional Tumor Invasion Model

Ito, Akio

22 ( 2 )  , pp.569 - 612 , 2015-03-31 , Graduate School of Mathematical Sciences, The University of Tokyo
We consider a one-dimensional tumor invasion model of Chaplain–Anderson type with quasi-variational structure, which is originally proposed in [3]. One object is to show the existence of globalin- time solutions by using the limit procedure for suitable approximate solutions. The other is to consider the asymptotic behaviors of globalin- time solutions as time goes to ∞. Actually, we construct at least one global-in-time solution, which enables us to consider the convergence to a certain constant steady-state solution as time goes to ∞ whenever the initial data satisfy suitable conditions.

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