Mathematical Analysis of Tumour Invasion Model with Proliferation and Re-Establishment

Abstract: We study the global existence in time and asymptotic profile of solutions of a mathematical model of tumour invasion proposed by Chaplain and Lolas. We consider related nonlinear evolution equations with strong dissipation, proliferation and an initial Neumann-boundary value problem. We show global existence in time of solutions to the initial boundary value problem in arbitrary space dimension by using the method of energy. Applying the result of existence and asymptotic behaviour of solutions to our problem we discuss the property of the solution to the tumour invasion model. Further we discuss a more general form of the nonlinear evolution equation, which could give the same type of existence theorem for a more general form of the tumour invasion model.