Constructive method for the Cauchy problem of parabolic equations and its mechanization;

Cauchy problem for a class of coupled hyperbolic systems of conservation laws;

The generalization of the sabstitution-iteration method for high-dimension wave equation s Cauchy problem;

The propagation of singularities of solutions to the Cauchy problems of a linear thermoelastic system for microstretch materials in one space variable is studied by using an argument of frequencies analysis.

In this paper, we investigate the following non-local Cauchy problem of nonlinear population evolution equation with random periodic migration perturbation,{(p(r,t))/(t)+(p(r,t))/(r)=-μ(r)p(r,t)+f(t,p(r,t)),0<r<rm,t0p(r,0)=p0(r)+g(p(r,t0)),T>t0>0 p(0,t)=β(t)integral from n=r1 to r2 k(r)h(r)p(r,t)dr, t≥0.

n-times integrated C-semigroups and abstract cauchy problem;

We also investigate the relations of n-times integrated C-semigroups and the strong solution of corresponding non-homogeneous abstract Cauchy problem, and the representation of strong solution.

We prove the one-to-one correspondence between mild solutions of a linear partial differential equation with delay and mild solutions of an associated abstract Cauchy problem, and give necessary and sufficient conditions for existence and uniqueness of mild solutions of the linear partial differential equation.