Xianfa Song

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All published works

Action	Title	Year	Authors
+ PDF Chat	Double thresholds for blowup and global existence phenomena occur in heat transfer	2024	Xianfa Song
+ PDF Chat	A spatial SIS model in heterogeneous environments with vary advective rate	2024	Xiaowei An Xianfa Song
+	Critical line of exponents, scattering theories for a weighted gradient system of semilinear wave equations	2024	Xianfa Song
+ PDF Chat	Weighted spacetime bounds and sharp threshold result for the solution of quasilinear Schr\”{o}dinger equation with critical Sobolev exponent	2022	Xianfa Song
+ PDF Chat	Spacetime estimates and scattering theory for quasilinear Schrodinger equations in arbitrary space dimension	2021	Xianfa Song
+	Critical exponents line, scattering thoeries for a weighted gradient system of semilinear Schrodinger equations	2021	Xianfa Song
+	$H^s_x\times H^s_x$ scattering theory for a weighted gradient system of 3D radial defocusing NLS	2021	Xianfa Song
+	A spatial SIS model in heterogeneous environments with vary advective rate	2021	Xiaowei An Xianfa Song
+	A free boundary problem for spreading under shifting climate	2020	Yuanyang Hu Xinan Hao Xianfa Song Yihong Du
+ PDF Chat	Stability of the standing wave solution to a quasilinear Schrödinger equation	2019	Xianfa Song Zhi-Qiang Wang
+	Morawetz estimates as well as spacetime bounds based on pseudoconformal conservation law and interaction Morawetz estimates for a quasilinear Schr\"{o}dinger equation	2019	Xianfa Song
+	Morawetz estimates and spacetime bounds for quasilinear Schrödinger equations with critical Sobolev exponent	2019	Xianfa Song
+	The role of potential, Morawetz estimate and spacetime bound for quasilinear Schrödinger equations	2019	Xianfa Song
+	Spacetime estimates and scattering theory for quasilinear Schrödinger equations in arbitrary space dimension	2019	Xianfa Song
+	How Hartree type nonlinearity takes effect on the properties for the solution of a quasilinear Schr\"{o}dinger equation	2018	Xianfa Song Zhiqiang Wang
+	The relationships between some types of partial differential equations and ordinary differential equations as well as their applications	2018	Xianfa Song Xiaoshuang Lv
+	Global existence, blowup phenomena, and asymptotic behavior for quasilinear Schrödinger equations	2018	Xianfa Song Zhi-Qiang Wang
+	A quasilinear Schrödinger equation with Hartree type nonlinearity	2018	Xianfa Song Zhi-Qiang Wang
+	Bounds for the blowup time and blowup rate estimates for a type of parabolic equations with weighted source	2014	Xianfa Song Xiaoshuang Lv
+ PDF Chat	Phenomena of Blowup and Global Existence of the Solution to a Nonlinear Schrödinger Equation	2013	Xiaowei An Desheng Li Xianfa Song
+	Some Results on the Scattering Theory for a Schrödinger Equation with Combined Power-Type Nonlinearities	2011	Xianfa Song
+ PDF Chat	Erratum to “Sharp thresholds of global existence and blowup for a system of Schrödinger equations with combined power-type nonlinearities” [J. Math. Phys. 51, 033509 (2010)]	2010	Xianfa Song
+	Remarks on Scattering Properties of the Solution to a Nonlinear Schr	2010	Xianfa Song
+	Sharp thresholds of global existence and blowup for a system of Schrödinger equations with combined power-type nonlinearities	2010	Xianfa Song
+	On the Global Existence and Blowup Phenomena of Schrödinger Equations with Multiple Nonlinearities	2010	Xianfa Song
+	Remarks on Scattering Properties of the Solution to a Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities	2010	Xianfa Song
+	Stability and instability of standing waves to a system of Schrödinger equations with combined power-type nonlinearities	2009	Xianfa Song
+	Gradient estimates for the elliptic and parabolic Lichnerowicz equations on compact manifolds	2009	Xianfa Song Lin Zhao
+ PDF Chat	ON GLOBAL ROUGH SOLUTIONS TO A NON-LINEAR SCHRÖDINGER SYSTEM	2009	Li L Xianfa Song Lin Zhao
+	Gradient estimate for the degenerate parabolic equation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mi>u</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>u</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mi>H</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>u</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:…	2007	Li Ma Lin Zhao Xianfa Song
+	Blow-up analysis for a system of heat equations with nonlinear flux which obey different laws	2007	Xianfa Song
+	New Monotonicity Formulae for Semi-linear Elliptic and Parabolic Systems	2005	Li Ma Xianfa Song Lin Zhao
+	Blow-up analysis for a nonlinear diffusion system	2004	Xianfa Song Sining Zheng Zhaoxin Jiang
+	Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux	2004	Sining Zheng Xianfa Song Zhaoxin Jiang
+	Blow-up analysis for a nonlinear diffusion equation with nonlinear boundary conditions	2004	Zhaoxin Jiang Sining Zheng Xianfa Song
+	Critical exponents in a parabolic system with inner absorption and coupled nonlinear boundary flux	2003	Sining Zheng Wenmiao Liang Xianfa Song
+	Blow-up and blow-up rate for a reaction–diffusion model with multiple nonlinearities	2003	Xianfa Song Sining Zheng
+	Blow-up analysis for a quasilinear parabolic system with multi-coupled nonlinearities	2003	Xianfa Song Sining Zheng

Common Coauthors

Coauthor	Papers Together
Sining Zheng	6
Lin Zhao	4
Zhaoxin Jiang	3
Zhi-Qiang Wang	3
Xiaoshuang Lv	2
Li Ma	2
Xiaowei An	2
Yihong Du	1
Zhiqiang Wang	1
Desheng Li	1
Xinan Hao	1
Li L	1
Yuanyang Hu	1
Xiaowei An	1
Wenmiao Liang	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	On a class of nonlinear Schr�dinger equations	1992	Paul H. Rabinowitz	10
+	On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations	1977	Robert T. Glassey	9
+ PDF Chat	The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities	2007	Terence Tao Monica Vişan Xiaoyi Zhang	6
+	On the Local Well Posedness of Quasilinear Schrödinger Equations in Arbitrary Space Dimension	2001	Markus Poppenberg	5
+	Global Solutions of Nonlinear Schrödinger Equations	1999	J. Bourgain	5
+	Global Existence of Small Solutions to a Relativistic Nonlinear Schrödinger Equation	1997	Anne de Bouard Nakao Hayashi Jean‐Claude Saut	5
+ PDF Chat	Partial Differential Equations	1988	Shiing-Shen Chern	5
+ PDF Chat	Global well-posedness and scattering for the energy-critical Schrödinger equation in ℝ<sup>3</sup>	2008	J. Colliander M. Keel Gigliola Staffilani Hideo Takaoka Terence Tao	5
+	Nonexistence of Positive Solutions to a Semilinear Elliptic System and Blow-up Estimates for a Reaction-Diffusion System	1999	Sining Zheng	5
+ PDF Chat	The asymptotic behavior of nonlinear Schrödinger equations	1984	Yoshio Tsutsumi Kenji Yajima	4
+	Sharp Threshold for Blowup and Global Existence in Nonlinear Schrödinger Equations Under a Harmonic Potential	2005	Jian Zhang	4
+	Nonlinear Parabolic and Elliptic Equations	1993	C. V. Pao	4
+	Global boundedness of solutions to a reaction-diffusion system	1999	Sining Zheng	4
+ PDF Chat	The profile near blowup time for solution of the heat equation with a nonlinear boundary condition	1994	Bei Hu Hong‐Ming Yin	4
+ PDF Chat	Stability and instability results for standing waves of quasi-linear Schrödinger equations	2010	Mathieu Colin Louis Jeanjean Marco Squassina	3
+	Global existence and global non-existence of solutions to a reaction-diffusion system	2000	Sining Zheng	3
+	The Cauchy problem for quasi-linear Schr�dinger equations	2004	Carlos E. Kenig Gustavo Ponce Luis Vega	3
+	Semilinear Schrödinger Equations	2003	Thierry Cazenave	3
+ PDF Chat	Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case	2006	Carlos E. Kenig Frank Merle	3
+	Critical blowup and global existence numbers for a weakly coupled system of reaction-diffusion equations	1995	Miguel Escobedo Howard A. Levine	3
+	Parabolic evolution equations and nonlinear boundary conditions	1988	Herbert Amann	3
+ PDF Chat	Sharp thresholds of blow-up and global existence for the coupled nonlinear Schrödinger system	2008	Li Ma Lin Zhao	3
+	Scattering for the non-radial 3D cubic nonlinear Schrödinger equation	2008	Thomas Duyckaerts Justin Holmer Svetlana Roudenko	3
+	Nonlinear dispersive equations	2006	徹小澤誉志雄堤	3
+	Nonlinear Schrodinger Equations at Critical Regularity	2013	Rowan Killip Monica Vi	3
+	Asymptotically self‐similar blow‐up of semilinear heat equations	1985	Yoshikazu Giga Robert V. Kohn	3
+ PDF Chat	The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions	2007	Monica Vişan	3
+	Linear and Quasi-linear Equations of Parabolic Type	1968	O. Ladyženskaja V. A. Solonnikov N. Ural’ceva	3
+	The “Blow up” problem for a quasilinear Schrödinger equation	2005	Boling Guo Jianqing Chen Fengqiu Su	3
+	On a class of non linear Schr�dinger equations with non local interaction	1980	J. Ginibre G. Velo	3
+	Diffusivity versus absorption through the boundary	1992	Ján Filo	3
+	The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions	2005	Monica Vişan	3
+ PDF Chat	Global existence and nonexistence for a parabolic system with nonlinear boundary conditions	1998	Julio D. Rossi Noemí Wolanski	2
+	Global existence and nonexistence for semilinear parabolic systems with nonlinear boundary conditions	1989	Joachim Escher	2
+ PDF Chat	Geometric Theory of Semilinear Parabolic Equations	1981	Daniel Henry	2
+ PDF Chat	Solitons and Scattering for the Cubic–Quintic Nonlinear Schrödinger Equation on $${\mathbb{R}^3}$$ R 3	2017	Rowan Killip Tadahiro Oh Oana Pocovnicu Monica Vişan	2
+	Nonlinear Schr�dinger equations and sharp interpolation estimates	1983	Michael I. Weinstein	2
+	Basic Reproduction Numbers for Reaction-Diffusion Epidemic Models	2012	Wendi Wang Xiao‐Qiang Zhao	2
+	The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher	2010	Rowan Killip Monica Vişan	2
+ PDF Chat	On global bifurcation for quasilinear elliptic systems on bounded domains	2008	Junping Shi Xuefeng Wang	2
+ PDF Chat	On the Harnack inequalities of partial differential equations	1994	Shing‐Tung Yau	2
+	ON THE LOCAL WELL-POSEDNESS OF QUASILINEAR SCHRÖDINGER EQUATIONS IN ARBITRARY SPACE DIMENSION	2002	Mathieu Colin	2
+	Partial Differential Equations of Parabolic Type	1964	Avner Friedman	2
+	Persistence and Bifurcation of Degenerate Solutions	1999	Junping Shi	2
+ PDF Chat	Uniqueness of the ground state solutions of quasilinear Schrödinger equations	2011	Shinji Adachi Tatsuya Watanabe	2
+	The nonlinear Schrödinger equation with combined power-type nonlinearities	2005	Terence Tao Monica Vişan Xiaoyi Zhang	2
+ PDF Chat	Global well-posedness and scattering for the mass-critical Hartree equation with radial data	2008	Changxing Miao Guixiang Xu Lifeng Zhao	2
+	Uniform blow-up rate for parabolic equations with a weighted nonlocal nonlinear source	2009	Jiang Liang-jun XU Yong-ping	2
+	Global Existence and Blow-Up Problems for Quasilinear Parabolic Equations with Nonlinear Boundary Conditions	1993	Mingxin Wang Yonghui Wu	2
+	Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time	1974	Howard A. Levine L. E. Payne	2