2 citations · 4 across the 15 of their papers we have counts for
10 papers · 1 filter
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…
A quasilinear Schrödinger equation with Hartree type nonlinearity
Xianfa Song, Zhi-Qiang Wang
In this paper, we deal with the Cauchy problem of the quasilinear Schödinger equation \begin{equation*} \left\{ \begin{array}{lll} iu_t=Δu+2uh'(|u|^2)Δh(|u|^2)+(W(x)\ast|u|^2)u,\ x…
Global existence, blowup phenomena, and asymptotic behavior for quasilinear Schrödinger equations
Xiaowei An, Xianfa Song
In this paper, we study the Cauchy problem of the quasilinear Schrödinger equation \begin{equation*} \left\{ \begin{array}{lll} iu_t=Δu+2uh'(|u|^2)Δh(|u|^2)+F(|u|^2)u \quad {\rm fo…
Some Results on the Scattering Theory for a Schrödinger Equation with Combined Power-Type Nonlinearities
Xianfa Song
In this paper, we consider the Cauchy problem {align*} \{{array}{ll}&i u_t+Δu=λ_1|u|^{p_1}u+λ_2|u|^{p_2}u, \quad t\in\mathbb{R}, \quad x\in\mathbb{R}^N &u(0,x)=ϕ(x)\in Σ, \quad x\i…
On the Global Existence and Blowup Phenomena of Schrödinger Equations with Multiple Nonlinearities
Xianfa Song
In this paper, we consider the global existence and blowup phenomena of the following Cauchy problem \begin{align*} \left\{\begin{array}{ll}&-i u_t=Δu-V(x)u+f(x,|u|^2)u+(W\star|u|^…
Remarks on Scattering Properties of the Solution to a Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities
Xianfa Song
In this paper, we consider the Cauchy problem of Nonlinear Schrödinger equation \begin{align*} \left\{\begin{array}{ll}&i u_t+Δu=λ_1|u|^{p_1}u+λ_2|u|^{p_2}u, \quad t\in\mathbb{R},…
New Monotonicity Formulae for Semi-linear Elliptic and Parabolic Systems
Li Ma, Xianfa Song, Lin Zhao
In this paper, we establish a general monotonicity formula of the following elliptic system $$ Δu_i+f_i(u_1,...,u_m)=0 \quad {\rm in} Ω, \label{0.1} $$ where $Ω\subset\subset \math…