一类强退化拟线性抛物方程的弱解

In this paper, we show the existence of the renormalized solutions and the entropy solutions of a class of strongly degenerate quasilinear parabolic equations.     

GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form of η(ρ)=ρ~α.The existence of unique global H^2m-solutions(m ∈ N) to the free boundary problem is proven for when 0 <α<1/4.Furthermore,we obtain the global C~∞-solutions if the initial data is smooth.     

Global Existence and Blow-up of Solutions to Multi-dimensional （n ≤ 5） Viscous Cahn-Hilliard Equation

In this paper we consider the viscous Cahn-Hilliard equation with spatial dimension n ≤5, and established global existence of weak solutions for small initial value and blow-up of solutions for any nontrivial initial data.