南方科技大学
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数学系
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学术会议
English
PDE Seminar
1970/01/01-1970/01/01
会议概要
On a semilinear elliptic equation arising from MEMS
Vortex solutions for Inhomogeneous Gross-Pitaevskii Equation in Three Dimensional Spaces
Seminar：A hyperbolic model in micro-electro-mechanical system
Some results on Kirchhoff type Problems
PDE Seminar：On the Free Surface Motion of Highly Subsonic Heat-Conducting Flows
2维不可压缩弹性力学方程的整体经典解
生态学模型的自由边界问题
The Large Deviation Principle and Steady-state Fluctuation Theorem for the Entropy Production Rate of a Stochastic Process in Magnetic Fields
Basic results for incompressible Navier-Stokes equations
Recent progress on classical solutions for compressible isentropic Navier-Stokes equations with degenerate viscosities and vacuum
Global well-posedness of the Boltzmann equation with large amplitude initial data
Measure valued solutions to spatially homogenous Boltzmann equation
Linearized and nonlinear numerical stability for nonlinear PDEs
Singular Limit of Symmetric Hyperbolic Systems
Compressible Navier-Stokes equations with degenerate viscosities
Nonlinear stability of localized and non-localized vortices in rotating compressible media
Stability of transonic flows past a wedge
ON EIGENVALUE PROBLEMS ARISING FROM NONLOCAL DIFFUSION MODELS
A double layer-averaged model for vertically concurrent shallow water flow and shallow water-sediment mixture flow
Kinetics models of chemotaxis with temporal sensing mechanism: the parabolic limit and its dynamics
Agent-based models exhibiting spatial aggregation
PDE Models of Morphogen Dynamics and Growth Control
Global dynamics of the MHD: nonlinear stability of Alfven waves
On Magnetic Inhibition Theory in Non-resistive MHD Fluids
Competitive Exclusion and Coexistence in a Two-Strain Pathogen Model with Diffusion
Variational methods and numerical simulations on the N-body problem of celestial mechanics
Spirals and heteroclinic cycles in a spatially extended Rock-Paper-Scissors model of cyclic dominance
Multiplicity and bifurcation of positive solutions for nonhomogeneous semilinear fractional Laplacian problems
Mathematical modeling of brain tumor growth with therapies
Non-isothermal electro-kinetics: energetic variational approach
Sign-changing Solutions for a Gauged Nonlinear Schrödinger Equation
Dynamics and Asymptotic Profiles of Steady States of an Epidemic Model in Advective Environments
Some recent progress on the limit of the principal eigenvalue of a time periodic parabolic operator
Dynamics and asymptotic profiles of endemic equilibrium for SIS epidemic patch models
GLOBAL DYNAMICS OF THE LOTKA-VOLTERRA COMPETITION SYSTEM WITH NONLOCAL DIFFUSION
On a diffusive host-pathogen system with different dispersal rates and spatial heterogeneity
几类扩散系统的传播动力学
The invertibility of Toeplitz Plus Hankel operators
A new geometric method and its applications in the N-body problem
Some mathematical analysis on the dynamical models for atmosphere with moisture
Global well-posedness and large time behavior of the compressible liquid-gas two-phase flow model
Some results on the free boundary problems for MHD
Free boundary value problem to 3D spherically symmetric compressible Navier–Stokes–Poisson equations
Axisymmetric Flow of Ideal Fluid Moving in a Narrow Domain
Estimates of eigenvalues for subelliptic operators on compact manifolds
Existence and stability of some nontrivial steady states for the SKT Competition model with large cross-diffusion
Mathematics in Ideal Free Distribution I
Mathematics in Ideal Free Distribution II
Centralizers of hyperbolic flows
Mini-course on Fluid Mechanics I: On the behavior of incompressible and inviscid planar fluid flow around a small disk
Mini-course on Fluid Mechanics II: On the behavior of incompressible and inviscid planar fluid flow around a small disk
Onsager-theory-based tensor model for nematic phases of bent-core molecules
Traveling Waves and Global Stability to Time-Delayed Reaction-Diffusion Equations with Degenerate Diffusion
Dynamics of Spike
Traveling Waves of Gray-Scott System: Results and Open Problems
Report on recent research works
Free interface problems arising in premixed flame propagation
Decay Estimates of Two Kinds of Problems in Fluid Mechanics
Littlewood-Paley Theory and Navier-Stokes systems I
Littlewood-Paley Theory and Navier-Stokes systems II
Littlewood-Paley Theory and Navier-Stokes systems III
Propagating Terrace and Asymptotic Profile to Time-Periodic Reaction-Diffusion Equations
Topics on PDE
Topics on PDE
Topics on PDE
Bounded Wave Solutions of the KdV-Burgers-Kuramoto Equation
Qualitative properties of the solution of a quasi-linear parabolic problem with a source term and a nonlocal absorption
Uniqueness and non-uniqueness of stationary solutions of aggregation-diffusion equation
Viscosity Solution to First Order Hamilton-Jacobi Equations and Applications I
Viscosity Solution to First Order Hamilton-Jacobi Equations and Applications II
Viscosity Solution to First Order Hamilton-Jacobi Equations and Applications III
Convergence in Power Law Nonlinear Scalar Field Equations
Hessian recovery based finite element methods for the Cahn-Hilliard equation
The asymptotic propagation speed of the Fisher-KPP equation with effective boundary condition on a road
Solutions for nonlinear Schrodinger equations in a conic singular space
Theory on Parabolic Equations
Theory on Parabolic Equations
Theory on Parabolic Equations
Theory on Parabolic Equations
Pullback dynamics of some nonlinear evolutionary equations with respect to some non-autonomous non-compact external forces
Integrable systems with peakons and cuspons
Finite Codimensionality Technique in Optimization and Optimal Control Problems
Global small solutions to the MHD with some kinds of dissipation terms
3-reduction of the KP hierarchy and complete classification of soliton solutions for the “good" Boussinesq equation
An extension of Calderon-Zygmund type singular integral
The equations of the multi-phase humid atmosphere expressed as a quasi variational inequality
Global well-posedness on the 3D incompressible Navier-Stokes and Euler equations in orthogonal curvilinear coordinate systems
Wave Equation with van der Pol Boundary Condition
Vanishing viscosity limit
Vanishing viscosity limit II
Vanishing dissipation limit of planar wave patterns to the multi-dimensional compressible Navier-Stokes equations
Prandtl Boundary Layer and Complex Fluids
Time-Periodic Solutions to Quasilinear Hyperbolic Systems with Time-Periodic Boundary Conditions
Time-Periodic Solutions to Quasilinear Hyperbolic Systems with Time-Periodic Boundary Conditions
Lojasiewicz-Simon Inequality and its Applications in PDEs I
Lojasiewicz-Simon Inequality and its Applications in PDEs II
Dissipation enhancing flows and applications
Concavity of principal eigenvalue for linear second order operators and its application in population dynamics
Recent Progress on Asymptotic Stability for 2d Euler Equations
Uniform structural stability of Poiseuille flows in a pipe under Navier boundary conditions
Well-posedness of Navier-Stokes equations with vacuum but without compatibility conditions
【系列报告】Spatial decay and stability of traveling waves for some reaction diffusion models
【系列报告】Mathematical analysis of the vortex sheet problem
Wong-Zakai type approximations of rough random dynamical systems by smooth noise
Enhanced Dissipation and Transition Threshold for the 2-D Plane Poiseuille flow via Resolvent Estimate
Analysis of Mechano-Chemical Models of Vasculogenesis
Global Dynamics of a Predator-Prey Model in Open Advective Environments
Taxis-driven formation of hotspots in a cross-diffusion model for virus infection
Hartree equation in the Schatten class
Modeling Immunity to Malaria with an Age-Structu red PDE Framework
Soliton Resolution for Wave Type Equations for Wave Type Equations
【短期课程】Elliptic and Parabolic Equations
Systems of semi-linear wave equations with multiple speeds in two space dimensions and a weaker null condition
Landau Damping for the Vlasov-Poisson system
Control of parabolic equations with inverse square infinite potential wells
Structural stability of interior subsonic steady-states to hydrodynamic model for semiconductors with sonic boundary
Finite time blow up and lifespan estimate for semilinear wave equations in Schwarzschild spacetime
Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data
Zero-dispersion limit for the Benjamin-Ono equation on the torus
The global stability of the Kaluza-Klein spacetime
Invariant Gibbs measures for 2D NLS and 3D cubic NLW
Stability of biological patterns to the chemotaxis models
Dynamics of the Landau-Lifshitz flows
On the long time behavior of nonlinear dispersive equations and related problems
Some big bangs are unstable
Propagation Phenomenon of Nonlocal Reaction-Diffusion Model with Bounded Phenotypic Traits
A Delay Induced Nonlocal Free Boundary Problem
Locally constrained inverse curvature flows and applications
Optimal Regularity for a Signorini-Type Gradient Degenerate Problem
Small Scale Creation for 2D Water Waves
On Isometric Immersions with Low Regularity
Propagation of Smallness for Solutions of 2D Elliptic Equations
Localization Estimates for Quantum Dynamics
Sharp regularity estimates for the collisional kinetic equations
Global stability of the Minkowski spacetime for the Einstein-Vlasov system
Multiplicity of Solutions for Quasilinear Elliptic Equations
传染病模型中的停时、峰值和风险指标
Weak Diffusive Stability Induced by High-Order Spectral Degeneracies
Global theory of nonlinear Schrodinger equations in the weighted space
Super Liouville equations on surfaces
Part I: The local well-posedness of the water wave equations
Dynamics of a consumer-resource model in a two-patch environment
On the Cauchy problem for the nonlinear Schrödinger equation on the two sphere
On a Mathematical Model Arising from an Optimal Chemotherapeutic Drug Treatment for Tumor Cells
临界John问题新探
The sharp estimate of nodal sets for Dirichlet Laplace eigenfunctions in polytopes
Part I: Two conformal compactifications of Minkowski spacetime
Part II: Schwarzschild’s spacetime, its maximal extension and conformal compactification
Part III: Conformal wave equation and Friedlander’s radiation fields
Part IV: Lax-Phillips theory
Global well-posedness and scattering for the massive Dirac-Klein-Gordon system in two space dimensions
临界John问题新探
Abstract
经典的John问题给出了幂次型非线性波动方程解的临界指标。本报告中，我们将从一般的非线性函数的角度出发重新探讨John问题的临界行为，并由此给出几乎最优的临界非线性结果以及猜测。该报告基于与张笑然博士的合作。