In this paper, we study a class of nonlinear higher order partial differential equations with irregular singularities in complex domain Ct

In this paper, we first go over some aspects of paradifferential calculus in Gevrey classes, then study some propositions of symbols related to fully nonlinear partial differential equations in Gevrey classes, and as an application, get Gevrey microregularity of solutions at elliptic points.

In this paper we study the global in-time and blow-up solutions for the simplified Keller-Segel system modelling chemotaxis. We prove that there is a critical number which determines the occurrence of blow-up in two dimensional case for 1＜p＜2. In three or higher dimensional cases, we show that the radial symmetrical solution will be blow up if 1＜p＜N/N-2 (N≥3) for nonnegative initial value.

In this paper, we study a parabolic-elliptic system defined on a bounded domain of R3, which comes from a chemotactic model. We first prove the existence and uniqueness of local in time solution to this problem in the Sobolev spaces framework, then we study the norm behavior of solution, which may help us to determine the blow-up norm of the maximal solution.

In this paper, we study the local existence and uniqueness of classical solutions to a wide class of systems of chemotaxis equations. These systems are essentially quasilinear strongly coupled partial differential equations. We also study the maximal interval of existence in time of solutions. The results are illustrated in application to a number of partial differential equation models arising in biology.