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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The C0 estimate of the cscK equation
cscK方程 C0估计 ABP最大值原理
2023/11/13
We report the work of Chen-Cheng on the existence of cscK metrics. In this talk I will mainly focus on the C0 estimate, which is derived using the ABP maximum principle.
On the prescribing σ2 curvature equation on S 4
σk curvature prescribing curvature fully nonlinear curvature equation
2014/4/3
Prescribing σk curvature equations are fully nonlinear generalizations of the prescribing Gaussian or scalar curvature equations. For a given a positive function K to be prescribed on the 4-dimensiona...
A Class of Special Solutions for the Ultradiscrete Painleve II Equation
ultradiscretization Painleve equation Airy equation q-difference equation
2011/10/9
Abstract: A class of special solutions are constructed in an intuitive way for the ultradiscrete analog of $q$-Painlev\'e II ($q$-PII) equation. The solutions are classified into four groups depending...
Celebrating Cercignani's conjecture for the Boltzmann equation
Cercignani’s conjecture spectral gap Boltzmann equation relative entropy
2010/12/9
Cercignani’s conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann’s nonlinear integral operator in rarefied gas dynamics. Related to the field of...
New Exact Solutions of a Generalized Shallow Water Wave Equation
Exact Solutions Generalized Shallow Water Wave Equation
2010/4/2
In this work an extended Jacobian elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave s...
Classification of conservative hydrodynamic chains. Vlasov type kinetic equation, Riemann mapping and the method of symmetric hydrodynamic reductions
hydrodynamic chains kinetic equation hydrodynamic reductions
2010/4/7
A complete classification of integrable conservative hydrodynamic chains is presented. These hydrodynamic chains are written via special coordinates -- moments, such that right hand sides of these inf...
One—．parameter optimal systems for the nonllnearevolutlon equation
Lie group Of symmetry optimal system adjoint representation nonlinear evolution equation
2009/10/29
The symmetry algebras of 1+ 1 dimensional nonlinear evolution equation arising from the motion of plane curve in affine geometry are systematically studied．It is found that the equation admits a seven...
On a Certain Volterra-Fredholm Type Integral Equation
Volterra-Fredholm type integral equation Banach fixed point theorem integral inequality Bielecki type norm existence and uniqueness continuous dependence
2010/1/22
The aim of this paper is to study the existence, uniqueness and other properties of solutions of a certain Volterra-Fredholm type integral equation. The main tools employed in the analysis are based o...
Regularity of Solutions of the Cahn-Hilliard Equation with non-Constant Mobility
Cahn--Hilliard equation regularity Schauder estimates
2007/12/12
In this paper, we study the regularity of solutions for two-dimensional Cahn--Hilliard equation with non-constant mobility. Basing on the $L^p$ type estimates and Schauder type estimates, we prove the...
Positive and Nontrivial Solutions for the Urysohn Integral Equation
Urysohn integral equation positive solutions eigenvalues
2007/12/12
We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficien...
Mixed Type of Integral Equation with Potential Kernel
Fredholm integral equations Potential kernel Legendre and Jacobi polynomials Weber-Sonien integral
2010/2/25
This paper presents the solution of an integral equation of a mixed type in three-dimensions in the space L2 (W) \times C[0,T], where T < \infty, and W is the domain of integration with respect to pos...
Numerical Solution and Convergence Speed of Variational Formulation for Linear Schrödinger Equation
Optimal control problem Finite difference method Inverse problem
2010/3/1
This paper presents a numerical solution of an optimal control problem for linear parabolic equations. The estimates for the error of the difference scheme and the speed of convergence have been estab...
On The Solution of the E.P.D. Equation Using Finite Integral Transformations
Hyperbolic equations initial boundary value problems
2010/3/5
In this paper, a solution is given for the following initial boundary value problem: D=utt+k/t+ut+g(x, t) (t>0) u(0, t)=u(a, t)=0 u(x, 0)=f(x), ut(x, 0)=0 where x, a e Rn, t is the time variable, k < ...