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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
2023/12/11
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.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent progress on steady Prandtl equation and Tollmien-Schlichting waves
稳定 Prandtl方程 Tollmien-Schlichting波
2023/11/9
The Prandtl equation introduced by Prandtl in 1904 is a basic equation describling the behavior of the fluid near the boundary at high Reynolds number regime. In this talk, I will first introduce some...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stokes phenomenon and isomonodromy deformation equations: Explicit solution to the Riemann-Hilbert problem and integrability of the isomonodromy equation
斯托克斯现象 等单向变形方程 黎曼-希尔伯特问题 显式解 单场方程 可积性
2023/5/6
Stokes phenomenon states that the asymptotic behavior of functions can differ in different regions of the complex plane, and that these differences can be described in a quantitative way. These quanti...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Differential Equation Modeling Nesterov’s Accelerated Gradient Method
2015/7/8
We derive a second-order ordinary differential equation (ODE), which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can...
Multi-hump solitary waves of nonlinear Dirac equation
Nonlinear Dirac equation Solitary wave
2014/9/26
This paper concentrates on a (1+1)-dimensional nonlinear Dirac (NLD) equa-tion with a general self-interaction, being a linear combination of the scalar,
pseudoscalar, vector and axial vector self-in...
Based on the method of reduction to absurdity, I convert the Fermat Equation into an open curve, which is inequivalent to the elliptic curve Professor Wiles deduced through “making out cubic curve”.
Based on the method of reduction to absurdity, I convert the Fermat Equation into an open curve, which is inequivalent to the elliptic curve Professor Wiles deduced through “making out cubic curve”.
Symmetry Analysis for a Generalized Kadomtsev-Petviashvili Equation
generalized Kadomtsev-Petviashvili equation Lie algebra arbitrary functions
2010/4/2
A generalized Kadomtsev-Petviashvili equation (GKPE) $(u_t+u u_x + \beta(t)u +\gamma(t)u_{xxx})_x+\sigma(t)u_{yy}\ = \ 0$ is shown to admit an infinite-dimensional Lie group of symmetries when $\bt(t)...
Vertex operator for the non-autonomous ultradiscrete KP equation
Vertex operator non-autonomous ultradiscrete KP equation
2010/4/7
We propose an ultradiscrete analogue of the vertex operator in the case of the ultradiscrete KP equation--several other ultradiscrete equations--which maps N-soliton solutions to N+1-soliton ones.
EXISTENCE OF RADIAL SOLUTIONS FOR A FOURTH ORDER PARABOLIC EQUATION
Fourth order parabolic equation Radial solution Existence
2008/11/26
We consider an initial-boundary problem for a fourth order nonlinear parabolic equation.
The problem as a model arises in epitaxial growth of nanoscale thin films. Relying
on some necessary uniform ...
OSCILLATION OF A SECOND-ORDER DIFFERENCE EQUATION WITH A NONLINEAR DAMPED TERM IN ARCHIMEDEAN SPACE
Order relation second-order difference equation oscillation
2008/11/26
In Archimedean space (X;Á) we study oscillation of all solutions of the second-order
difference equation with a nonlinear damped term of the form
a(k)D2y(k)+b(k)Dy(k)+c(k)y(k)+ f (k;y(k);y(k&...
ATTRACTOR OF THE NONLINEAR SCHR ¨O DINGER EQUATION
Nonlinear Schr¨odinger equation Global attractor Regularity
2008/11/26
In this paper the regularity of the global attractor for the nonlinear Schr¨odinger equation
with potential is proved, i.e., the attractor is a bounded subset of a smaller functional
space.
APPLICATION OF ADOMIAN DECOMPOSITION METHOD TO SOLVING THE DUFFING-VAN DER POL EQUATION
Duffing-van der Pol equation Adomian decomposition method regular perturbation method
2008/11/26
In this paper, the Adomian decomposition method and the regular perturbation
method are used to study the Duffing-van der Pol equation. The two series solutions
obtained by each method are compared.
Estimates of Positive Solutions to a Boundary Value Problem for the Beam Equation
Positive solution boundary value problem beam equation upper and lower estimates
2008/11/25
We consider a two-point boundary value problem for the fourth order beam equation.
New upper and lower estimates of positive solutions of the problem are obtained.
A Computational Approach to Study a Logistic Equation
Logistic equation Positive solutions Finite difference method
2008/11/25
Using a numerical method, we will show the existence of multiple solutions for the
well known logistic equation −u = λf (x)u(1 − u) for x ∈ , with Dirichlet boundary
condition.