Global Regularity versus Infinite-Time Singularity Formation in a Chemotaxis Model with Volume-Filling Effect and Degenerate Diffusion
Global Regularity versus Infinite-Time Singularity Formation in a Chemotaxis Model with Volume-Filling Effect and Degenerate Diffusion
复制标题
DOI：
10.1137/110853972
复制
发表时间：
2012-10
期刊：
影响因子：
--
通讯作者：
Zhian Wang;M. Winkler;D. Wrzosek
中科院分区：
文献类型：
--
作者：
Zhian Wang;M. Winkler;D. Wrzosek
研究一类描述趋化性的拟线性抛物型和椭圆抛物型方程组。由于假设存在体积填充效应，因此假设细胞密度存在无法通过的阈值。这种假设导致奇异或退化运营商在扩散和趋化组件的流量的细胞。我们从早期的作品，并找到反映扩散和趋化性之间的相互作用的临界条件，并保证经典的解决方案是全球性的时间和分离的阈值一致。在退化扩散的情况下，椭圆-抛物型版本的模型，我们证明了存在的径向对称的解决方案，表现出的现象，无限时间奇异性的形成，他们是全球性的和光滑的，但达到阈值的大的时间限制。
A system of quasi-linear parabolic and elliptic-parabolic equations describing chemotaxis is studied. Due to the assumed presence of a volume-filling effect it is assumed that there is an impassable threshold for the density of cells. This assumption leads to singular or degenerate operators in both the diffusive and the chemotactic components of the flux of cells. We improve results from earlier works and find critical conditions which reflect the interplay between diffusion and chemotaxis and warrant that classical solutions are global in time and separated uniformly from the threshold. In the case of degenerate diffusion for the elliptic-parabolic version of the model we prove the existence of radially symmetric solutions which exhibit a phenomenon of infinite-time singularity formation in that they are global and smooth but attain the threshold in the large time limit.