一类抛物型趋化模型的解的存在性

EXISTENCE OF SOLUTION TO A PARABOLIC CHEMOTAXIS MODEL

本文研究了一类抛物型趋化模型的解的存在性问题.利用算子半群理论,Sobolev嵌入定理及不等式技巧对解进行一些重要的先验估计,然后构造压缩映射证明了模型存在局部解.进一步构造迭代估计来说明不可能存在爆破,从而证明全局解的存在.

In this paper, we study the existence of solution to a parabolic chemotaxis model. First, some crucial priori estimates have been gotten utilizing semigroup theory, Sobolev imbedding and technics in inequality, then fixed point theorem is applied to prove the existence of local solution by constructing a contraction mapping. At last, we prove the global existence by one iteration to show no blow-up occurring.