Asymptotic Character Of Solution Of Reaction-diffusion Equation

In this paper,we study a mathematical model of cancer invasion proposed by Gatenby and Gawlinski.The model is a strongly coupled degenerate reaction-diffusion system.Under the assumption thatα₁₂ andα₂₁ is not zero,we make rigorous mathematical analysis to this model and obtain the following two results:on the one hand,Global existence of solutions.H.Amann's existence theorem for generalized quasilinear parabolic equations and integral estimate method,We prove that this model has a unique global solutions by using approximation method,the key point is to establish integral estimate of solution of this model.on the other hand,Asymptotic behavior of solutions.By precisely constructing Lyapunov functions,we prove that all solutions will converge to a stationary solution as time goes to infinity.