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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...
Compact Central WENO Schemes for MultiDimensional Conservation Laws
hyperbolic systems central difference schemes high-order accuracy nonoscillatory schemes WENO reconstruction CWENO reconstruction
2015/10/8
We present a new third-order central scheme for approximating solutions of systems of conservation laws in one and two space dimensions. In the spirit of Godunov-type schemes, our method is based on r...
On the Behavior of the Total Variation in CWENO Methods for Conservation Laws
Hyperbolic conservation laws Central difference schemes High-order accuracy Non-oscillatory schemes CWENO reconstruction TVB
2015/10/8
We consider a family of high-order, weighted essentially non-oscillatory central schemes (CWENO) for approximating solutions of one-dimensional hyperbolic systems of conservation laws. We are interest...
Third-order 2D Central Schemes for Hyperbolic Conservation Laws
Two-dimensional framework system the law of conservation of two-dimensional euler equation the high resolution
2015/10/8
We extend a one-dimensional central-scheme first introduced by Liu and Tadmor, to the rather general framework of two-dimensional systems of conservation laws. This scheme is based on a two-dimensiona...
Moderate dispersion in scalar conservation laws
Travelling waves moderate dispersion Korteweg de Vries equation entropy solutions dissipative-dispersive scalar conservation laws
2015/7/14
We consider the weakly dissipative and weakly dispersive Burgers-Hopf-Korteweg-de-Vries equation with the diffusion coefficient ε and the dispersion rate δ in the range δ/ε → 0. We study thetravelling...
Exact Boundary Conditions for the Initial Value Problem of Convex Conservation Laws
exact boundary conditions artificial boundary conditions convex conservation laws Burgers’ (inviscid) equation
2015/5/4
The initial value problem of convex conservation laws, which includes the famous Burgers’ (inviscid) equation, plays an important rule not only in the-oretical analysis for conservation laws, but also...
Accuracy of Classical Conservation Laws for Hamilton PDES Under Runge-Kutta Discretizations
Accuracy of Classical Conservation Laws Hamilton PDES Runge-Kutta Discretizations
2012/8/7
We investigate conservative properties of Runge-Kutta methods
for Hamiltonian PDEs. It is shown that multi-symplecitic Runge-Kutta meth-
ods preserve precisely norm square conservation law. Based on...
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...
An extension of the modified Sawada-Kotera equation and conservation laws
fundamental mathematics spectralproblem integrable nonlinear evolution equations conservationlaws
2011/10/15
Based onthe modified Sawada-Kotera equation, we introduce a 3×3 matrix spectral problem with two potentials and derive a hierarchyof new nonlinear evolution equations. The second member in thehierarch...
Discrete conservation laws and port-Hamiltonian systems on graphs and complexes
conservation laws port-Hamiltonian systems graphs and complexes Optimization and Control
2011/9/1
Abstract: In this paper we present a unifying geometric framework for modeling various sorts of physical network dynamics as port-Hamiltonian systems. Basic idea is to associate with the incidence mat...
The matrix Lax representation of the generalized Riemann equations and its conservation Laws
generalized Riemann equation Saxton equation Lax representation
2011/7/5
It is shown that the generalized Riemann equation is equivalent with the
multicomponent generalization of the Hunter - Saxton equation. New matrix
and scalar Lax representation is presented for this...
New entropy conditions for scalar conservation laws with discontinuous flux
New entropy conditions scalar conservation laws discontinuous flux
2010/11/23
We propose new Kruzhkov type entropy conditions for one dimensional scalar conservation law with a discontinuous flux. We prove existence and uniqueness of the entropy admissible weak solution to the ...
A chain rule formula in BV and applications to conservation laws
chain rule formula BV conservation laws
2010/11/9
In this paper we prove a new chain rule formula for the distributional derivative of the composite function $v(x)=B(x,u(x))$, where $u:]a,b[\to\R^d$ has bounded variation, $B(x,\cdot)$ is continuousl...
$L^\infty(L^\infty)$-boundedness of DG($p$)-solutions for nonlinear conservation laws with boundary conditions
nonlinear conservation laws boundary conditions
2010/11/18
We prove the $L^\infty(L^\infty)$-boundedness of a higher-order shock-capturing streamline-diffusion DG-method based on polynomials of degree $p\geq 0$ for general scalar conservation laws. The estim...
On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
Symmetries Conservation laws Noether theorem Hamiltonian field theories
2010/12/6
This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian
systems in first-order classical field theories. Thus, we introduce a particular class of
symmetries and s...