中文摘要：

研究一个刻画癌细胞浸润其周围正常组织的带交叉扩散的偏微分方程模型整体解的存在性.该模型着重描述癌细胞、基质降解酶以及正常组织三者之间的相互作用.由于此模型中癌细胞密度和基质密度的空间正则性是"强耦合"的,因此利用基质重组中的竞争项来克服趋触项所带来的分析困难.利用特殊的组合估计、L~p-估计和Moser迭代技巧建立一系列解的先验估计,从而证明解的整体存在性.

英文摘要：

The global existence of classical solutions to a PDE with cross‐diffusion is considered , w hich describe the process of cancer cell invasion of surrounding tissue .T he model reflects the interactions between cancer cell ,enzyme and the tissue .In this mathematical model ,the cancer cell density and the tissue density is strong coupling .To overcome the afore said technical ob‐stacle ,the disadvantage of the haptotaxis term can be balanced by the competition of tissue re‐modeling term in a certain sense .A series of a priori estimates are established based on specific combined estimate ,Lp‐estimate and the Moser iteration method ,and the global existence of so‐lution is proved .