Asymptotic Behavior And Global Existence For A Haptotaxis Model Of Cancer Invasion With Tissue Regeneration

This paper deals with the global existence and the asymptotic behavior of solu-tions to a haptotaxis model of cancer invasion with tissue regeneration.The math-ematical model was initially proposed by Chaplain and Anderson[Cancer Modelling and Simulation,Chapman&Hall/CRT(2003),267-297],and it consists of a system of reaction-diffusion-taxis partial differential equations describing the interactions be-tween cancer cells,the matrix degrading enzymes secreted by cancer cells,and the host tissue.Under some assumptions on the initial data and the model parameters,it is proved that the global solution converges to a non-zero spatially uniform steady state exponentially as time goes to infinity.