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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Kazdan-Warner equations on compact Riemann surfaces
紧黎曼曲面 卡兹丹-华纳方程 数学
2023/4/28
In this talk, we shall review firstly the study history of Kazdan-Warner equations on compact Riemann surfaces, which was proposed by Kazdan and Warner on Annals of Math on 1974. Then we shall show th...
DIFFERENTIAL HARNACK ESTIMATES FOR TIME-DEPENDENT HEAT EQUATIONS WITH POTENTIALS
EQUATIONS WITH POTENTIALS DIFFERENTIAL HARNACK
2015/8/17
In this paper, we prove a differential Harnack inequality for positive
solutions of time-dependent heat equations with potentials. We also prove a gradient
estimate for the positive solution o...
Resonance and Landesman-Lazer condition for some Fully Nonlinear Elliptic equations
Resonance and Landesman-Lazer condition Nonlinear Elliptic equations
2015/4/3
Resonance and Landesman-Lazer condition for some Fully Nonlinear Elliptic equations.
In this artile we review some reent work on fourth order equations in onformal geometry of three and four dimensions. We dis uss some an existene result for a Yamabe-type equation in dimension three. ...
An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations
Inviscid model, singularity explicit solutions 2D Boussinesq equations
2014/4/3
We give an example of a well posed, nite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce nite time sing...
Minimal surface systems, maximal surface systems, and special Lagrangian equations
minimal submanifold special Lagrangian equation entire solution
2012/4/17
We extend Osserman's lemma on the generalized Gauss map of two-dimensional minimal graphs of higher codimension, construct a Jenkins-Serrin type special Lagrangian Scherk graph explicitly, and general...
Estimates on the modulus of expansion for vector fields solving nonlinear equations
Estimates vector fields nonlinear equations Differential Geometry
2011/9/5
Abstract: By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Sch\"ordinger operator with convex potential, wh...
Schrodinger equations, deformation theory and $tt^*$-geometry
Schrodinger equations deformation theory Differential Geometry
2011/8/26
Abstract: This is the first of a series of papers to construct the deformation theory of the form Schr\"odinger equation, which is related to a section-bundle system $(M,g,f)$, where $(M,g)$ is a nonc...
The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients
The Harnack inequality related properties elliptic
2010/11/15
We discuss the problem how "bad" may be lower-order coefficients in elliptic and parabolic second order equations to ensure some qualitative properties of solution such as strong maximum principle, H...
Wheeler-Feynman Equations for Rigid Charges - Classical Absorber Electrodynamics Part II
Maxwell-Lorentz Equations Maxwell Solutions Li´ enard-Wiechert fields
2010/12/7
This is the second part of our mathematical survey on the equations of motion of classical absorber electrodynamics. Here we study the equations of Wheeler-Feynman (WF) electrodynamics, which describe...
Coupling solutions of BGG-equations in conformal spin geometry
overdetermined systems conformal spin geometry twistor spinors conformal Killing fields conformal Killing forms
2010/12/1
BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and su...
Two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations
Camassa–Holm equation Degasperis–Procesi equation semidirect product geodesic flow
2010/11/26
We use geometric methods to study two natural two-component generalizations of the periodic Camassa–Holm and Degasperis–Procesi equations.
Exponential convergence to equilibrium for kinetic Fokker-Planck equations on Riemannian manifolds
kinetic Fokker-Planck equations Riemannian manifolds
2010/12/13
A class of linear kinetic Fokker-Planck equations with a non-trivial dif-fusion matrix and with periodic boundary conditions in the spatial vari-able is considered. After formulating the problem in a ...
Dynamics of soliton-like solutions for slowly varying, generalized gKdV equations: refraction vs. reflection
gKdV equations integrability theory soliton dynamics slowly varying medium
2010/12/13
In this work we continue our study of the description of the soliton-like solutions of the variable coecients, subcritical gKdV equation ut + (uxx u + a("x)um)x = 0; in Rt Rx; m = 2; 3 ...
Integrable GL(2) Geometry and Hydrodynamic Partial Differential Equations
Integrable GL(2) Geometry Hydrodynamic Partial Differential Equations
2010/4/7
This article is a local analysis of integrable GL(2)-structures of degree 4. A GL(2)-structure of degree n corresponds to a distribution of rational normal cones over a manifold M of dimension (n+1). ...