2 citations · 4 across the 15 of their papers we have counts for
16 papers
Three Homoscedastic Gaussian Components Have at Most Four Modes
Rintaro Okahara, Kei Kobayashi
Gaussian mixtures can have more modes than components. For three Gaussian components with a common covariance, four modes are attainable, whereas the best general upper bound was e…
Critical line of exponents, scattering theories for a weighted gradient system of semilinear wave equations
Xianfa Song
In this paper, we consider the following Cauchy problem of a weighted gradient system of semilinear wave equations \begin{equation*} \left\{ \begin{array}{lll} u_{tt}-Δu=λ|u|^α|v|^…
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…
Spacetime estimates and scattering theory for quasilinear Schrödinger equations in arbitrary space dimension
Xianfa Song
In this paper, we consider the following Cauchy problem of \begin{equation*} \left\{ \begin{array}{lll} iu_t=Δu+2δ_huh'(|u|^2)Δh(|u|^2)+V(x)u+F(|u|^2)u+(W*|u|^2)u,\ x\in \mathbb{R}…
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…
Linking Theorems of Local Semiflows on Complete Metric Spaces
Desheng Li, Guoliang Shi, Xianfa Song
In this paper we prove some linking theorems and mountain pass type results for dynamical systems in terms of local semiflows on complete metric spaces. Our results provide an alte…
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…