一维Chemotaxis模型双曲组的解的存在性及其抛物组的行波解

研究了一类简化的 Keller- Segel模型 pt=εpxx+ a( pwxw) x,wt=λpw- b w,x∈ R,t>0 ,按照 ε=0和 ε>0两种不同的情况模型进行讨论 .当 ε=0时 ,采用特征的方法 ,通过计算特征值与黎曼不等式 ,给出问题存在局部解且不可能有整体解的一个充分条件 .当 ε>0 ,给出了它的行波解的一个形式表达式 .     

B值鞅遍历定理与极大不等式

研究一类具有较强物理背景的B值鞅遍历过程.利用DooB上穿不等式,证明了其取值的Banach空间具有RN（Radon-Nikodym）性质时这类随机过程的收敛性.对于像空间为p-可光滑Banach空间的情况,综合利用鞅极大不等式和遍历极大不等式,证明了鞅遍历过程的一些极大不等式.     

Improved Gagliardo-Nirenberg inequalities on Heisenberg type groups

Motivated by the idea of M. Ledoux who brings out the connection between Sobolev embeddings and heat kernel bounds, we prove an analogous result for Kohn’s sub-Laplacian on the Heisenberg type groups. The main result includes features of an inequality of either Sobolev or Galiardo-Nirenberg type.     

CONVERGENCE THEOREMS AND MAXIMAL INEQUALITIES FOR MARTINGALE ERGODIC PROCESSES

In this article, we study two types of martingale ergodic processes. We prove that a.e. convergence and L^p convergence as well as maximal inequalities, which are established both in ergodic theory and martingale setting, also hold well for these new sequences of random variables. Moreover, the corresponding theorems in the former two areas turn out to be degenerate cases of the martingale ergodic theorems proved here.     

两类Chemotaxis模型解的性质

本文讨论了抛物-双曲和抛物-常微两个Chemotaxis模型初边值问题解的性质.利用形式级数展开的方法，得到全局解在微小扰动下，导致解在有限时间内爆破，并对爆破时间进行了估计.因此说明了这种模型空间齐性解的不稳定性。