1 citations · 1 across the 6 of their papers we have counts for
10 papers
scattering theory for a weighted gradient system of 3D radial defocusing NLS
Xianfa Song
In this paper, using -method, we establish scattering theories for the following Cauchy problem \begin{equation*} \left\{ \begin{array}{lll} iu_t+Δu=λ|v|^2u,…
Critical exponents line, scattering thoeries for a weighted gradient system of semilinear Schrodinger equations
Xianfa Song
We establish the local wellposedness of different type of solutions the system with different types of initial data. We find there exists a critical exponents line in space dimensi…
Quenching, global existence and blowup phenomena in heat transfer
Xianfa Song
Basing on the relations between a system of ODE and a system of parabolic equations, we establish some general theories in heat transfer about quenching, global existence and blowu…
A free boundary problem for spreading under shifting climate
Yuanyang Hu, Xinan Hao, Xianfa Song +1
In this paper we consider a free boundary problem which models the spreading of an invasive species whose spreading is enhanced by the changing climate. We assume that the climate…
The role of potential, Morawetz estimate and spacetime bound for quasilinear Schrödinger equations
Xianfa Song
In this paper, we deal with the following Cauchy problem \begin{equation*} \left\{ \begin{array}{lll} iu_t = Δu + 2uh'(|u|^2)Δh(|u|^2) + V(x)u,\ x\in \mathbb{R}^N,\ t>0\\ u(x,0) =…
Morawetz estimates and spacetime bounds for quasilinear Schrödinger equations with critical Sobolev exponent
Xianfa Song
In this paper, we study the following Cauchy problem \begin{equation*} \left\{ \begin{array}{lll} iu_t=Δu + 2uh'(|u|^2)Δh(|u|^2) + F(|u|^2)u\mp A[h(|u|^2]^{2^*-1} h'(|u|^2)u,\ x\in…