6 citations · 38 across the 25 of their papers we have counts for
25 papers
Modification to Maxwell's Equations
Shangbin Cui
A fixed electric charge is an electric current relative to a moving magnetic field, so that it is subjected to the force of the moving magnetic field. This means that not only time…
On the Banach manifold of simple domains in the Euclidean space and applications to free boundary problems
Shangbin Cui
In this paper we study the Banach manifold made up of simple -domains in the Euclidean space . This manifold is merely a topological or a Banach manifold…
Analysis of a free boundary problem modeling the growth of necrotic tumors
Shangbin Cui
In this paper we make rigorous mathematical analysis to a free boundary problem modeling the growth of necrotic tumors. A remarkable feature of this free boundary problem is that i…
Quasi-differentiable Banach manifold and phase-diagram of invariant parabolic differential equation in such manifold
Shangbin Cui
The purpose of this paper is twofold. First we study a class of Banach manifolds which are not differentiable in traditional sense but they are quasi-differentiable in the sense th…
Linearized stability theorem for invariant and quasi-invariant parabolic differential equations in Banach manifolds with applications to free boundary problems
Shangbin Cui
If a differential equation in a Banach manifold is invariant or quasi-invariant under the action of one or more Lie groups, then its stationary points cannot be isolated, so that c…
Sharp well-posedness and ill-posedness in Fourier-Besov spaces for the viscous primitive equations of geophysics
Jinyi Sun, Shangbin Cui
We study well-posedness and ill-posedness for Cauchy problem of the three-dimensional viscous primitive equations describing the large scale ocean and atmosphere dynamics. By using…