2015-03-31 , Graduate School of Mathematical Sciences, The University of Tokyo , Faculty of Engineering, Kinki University
We consider a one-dimensional tumor invasion model of Chaplain–Anderson type with quasi-variational structure, which is originally proposed in . 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.