The Existence Of Solutions For Trophoblast Invasion

Mathematical has been widely used in the biomedical field. The invasion phenomenonincluded the tumor cell invasion, has been attracted many scientists’ attention. Our paperstudies about the trophoblast invasion.The placenta plays an important role during mammalian pregnancy. During embry-onic development，the key link is that the trophoblast cells invade the uterine issue. Theextravillous cytotrophoblasts (EVCT) from the embryonic primitive trophoblastic cells，play the role like the process of the tumour cells invading the organisms. By invading theuterus matrix，the embryo successfully attached to the uterine，the trophoblast cells prolif-erate and migrate as a continuous at the same time，and the embroyo gradually developmentto the feths.In this paper，we mainly discuss the process of the chemotactic migration about thetrophoblast cells into the uterine tissue，which has an important function in the initial phaseof the mammalian pregnancy placental development，As the timescale of interest increase，the dominant migratory mechanism of the trophoblasts switches from chemotaxis to nonlin-ear random motion. We present and analyse a mathematical model，whereas in attentionfocussed on the existence of local solution by compression mapping principle and theglobal existence of solutions.The model can be seen as a particular predator-prey system，which contains four in-teraction equations，three cross-diffusion parabolic equation and an ordinary differentialequation model: This article is divided into four chapters.In the first chapter，we outlined the historical background of the development ofchemotaxis differential equations；In the second chapter，we introduced the prior knowledge of the paper，in order toexpound the inequalities and Some of the basic norm estimate．In the third chapter，we use the give the proof of the existence of local solution bycompression mapping principle in the banach space.In the fourth chapter，we analyze the global existence of solutions.