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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Low regularity conservation laws for the fifth-order modified KdV equations in Besov spaces
Besov空间 五阶修正KdV方程 低正则性 守恒定律
2023/4/19
We get a priori estimates for the fifth-order modified KdV equations in Besov spaces with low regularity which cover the full subcritical range. These estimates are obtained from the power series expa...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Non-local operators with low-order singular kernels
低阶 奇异内核 非局部 运算符 正则性估计 二阶椭圆方程
2023/4/24
The regularity estimates have well-established for second-order elliptic and parabolic equations, as well as for equations with stable-like non-local operators. Whether similar results hold for non-lo...
The Harnack inequality for second-order elliptic equations with divergence-free drifts
Harnack inequality second-order elliptic equations divergence-free drifts
2015/7/14
We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b ∈ Ln/2+δ ∩ L2 where δ > 0. As an application we provide a one ...
First-order SODE: OU processdX+aX(t)dt= dW(t)
Three options:a >0, a= 0, a <0.
First-order SPDE:du= au
xx dt+dW(t, x)
One option:a >0(Infinite-dimensional stable OU process.)
Second-order SODE:X¨ ...
Well-posedness for the fifth-order KdV equation in the energy space
Fifth-order KdV equation fifth-order water-waves models initial value problem
2012/5/9
We prove that the initial value problem (IVP) associated to the fifth order KdV equation {equation} \label{05KdV} \partial_tu-\alpha\partial^5_x u=c_1\partial_xu\partial_x^2u+c_2\partial_x(u\partial_x...
The Two-Component Camassa-Holm Equations CH(2,1) and CH(2,2): First-Order Integrating Factors and Conservation Laws
Two-Component Camassa-Holm Equations CH(2,1) CH(2,2) First-Order Integrating Factors Conservation Laws Exactly Solvable and Integrable Systems
2012/4/26
Recently, Holm and Ivanov, proposed and studied a class of multi-component generalisations of the Camassa-Holm equations [D D Holm and R I Ivanov, Multi-component generalizations of the CH equation: g...
Exact controllability for the fourth order Schr鰀inger equation
Fourth order Schr鰀inger equation HUM method Controllability Multiplier
2011/10/15
In this paper the boundary controllability of the fourth order Schr"odinger equation in bounded domains is studied. By means of a L2-Neumann boundary control, it is proven that the solution is exactly...
The Quenching Phenomena for Fourth-order Nonlinear Parabolic Equationos
Quenching phenomena fourth-order parabolic equation Quenching time
2011/10/15
In this paper, we investigate the quenching phenomena of initial boundary value problem for the fourth-order nonlinear parabolic equations in bounded domains. First, we not only obtain quenching pheno...
The quenching phenomena for second-order nonlinear parabolic equation with nonlinear source
Parabolic equation Quenching phenomena Unbounded domain
2011/10/15
In this paper, we investigate the quenching phenomena of the Cauchy problem for the second-order nonlinear parabolic equation on unbounded domain. It is shown that the solution quenches in finite time...
Stability of solitary waves for the generalized higher-order Boussinesq equation
Boussinesq equation solitary waves stability Analysis of PDEs
2011/9/19
Abstract: This work studies the stability of solitary waves of a class of sixth-order Boussinesq equations.
Refined Scattering and Hermitian Spectral Theory for Linear Higher-Order Schrodinger Equations
Higher-order Schrodinger operators rescaled blow-up variables discrete real spectrum asymptotic behaviour nodal sets of solutions
2011/9/9
Abstract: A classification of large-time and finite-time blow-up asymptotics of solutions of the Cauchy problem for higher-order Schr\"odinger equations is performed.
On a Fourth Order Lichnerowicz Type Equation Involving The Paneitz-Branson Operator
Fourth Order Lichnerowicz Type Equation Paneitz-Branson Operator
2011/2/24
In this paper, we study some fourth order singular critical equa-tions of Lichnerowicz type involving the Paneitz-Branson operator, and we prove existence and non existence results under given assumpt...
An Interior Gradient Estimate for a class of Second Order Partial Differential Inequalities
Interior Gradient Estimate class of Second Order Partial Differential Inequalities
2011/2/22
In this paper, we show a uniform gradient estimate for functions u defined on a domain
in Euclidian space RN which satisfy a system of N second order partial differential inequalities of the followi...
High order weak approximation schemes for Lévy-driven SDEs
Levy-driven stochastic di erential equation Euler scheme
2011/2/28
We propose new jump-adapted weak approximation schemes for stochas-tic di erential equations driven by pure-jump Levy processes.
Initial-boundary value problems for second order systems of partial differential equations
Initial-boundary value problems second order systems of partial differential equations
2011/1/18
We develop a well-posedness theory for second order systems in bounded domains where
boundary phenomena like glancing and surface waves play an important role. Attempts have previ-
ously been made t...