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TITLE Mathematical Analysis of Tumour Invasion Model with Proliferation and ReEstablishment 
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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 Neumannboundary 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. 
KEYWORDS Nonlinear evolution equation, mathematical analysis, tumour invasion, cell proliferation, reestablishment of MDE 
REFERENCES [1] Anderson,A.R.A. and Chaplain, M.A.J., Continuos and discrete mathematical models of tumourinduced angiogenesis, Bull. Math. Biol., 60 (1998), 857–899. [1] Anderson,A.R.A. and Chaplain, M.A.J., Continuos and discrete mathematical models of tumourinduced angiogenesis, Bull. Math. Biol., 60 (1998), 857–899. 
Cite this paper Akisato Kubo. (2016) Mathematical Analysis of Tumour Invasion Model with Proliferation and ReEstablishment. International Journal of Mathematical and Computational Methods, 1, 115119 
