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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The N-periodic wave solutions of some coupled bilinear equations
耦合 双线性方程 N周期波解
2023/4/26
In this talk, we present an efficient numerical scheme to calculate the N-periodic wave solutions to the Tzitzeica equation, the (2+1)-dimensional modified Bogoyavlenskii-Schiff equation and the mKdV-...
Fractional diffusion limit for collisional kinetic equations
fractional diffusion fractional heat equation anomalous heat transport linear Boltzmann equation relaxation equation linear BGK equation diffusion limit anomalous diffusion limit anomalous diffusive time scale mathematical derivation
2015/10/15
This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, t...
Perturbational Blowup Solutions to the 2-Component Camassa-Holm Equations
Perturbational Blowup 2-Component Camassa-Holm Equations
2011/1/19
In this article, we study the perturbational method to construct the non-radially symmet-ric solutions of the compressible 2-component Camassa-Holm equations. In detail, we first combine the substitut...
The Darboux coordinates for a new family of Hamiltonian operators and linearization of associated evolution equations
Hamiltonian operators bi-Hamiltonian systems evolution equations linearization
2011/1/20
A. de Sole, V. G. Kac, and M. Wakimoto have recently introduced a new family of compatible
Hamiltonian operators of the form H(N,0) = D2 ◦ ((1/u)◦D)2n ◦D, where N = 2n+3, n = 0, 1, ...
Factorizations and Reductions of Order in Quadratic and other Non-recursive Higher Order Difference Equations
non-recursive form symmetry factorization semi-invertible map criterion
2010/12/28
A higher order difference equation may be generally defined in an arbitrary nonempty set S as:
fn(xn, xn−1, . . . , xn−k) = gn(xn, xn−1, . . . , xn−k)where fn, gn: Sk+1→ S are...
Enhanced preliminary group classification of a class of generalized diffusion equations
Enhanced preliminary group classification class of generalized diffusion equations
2011/1/17
The method of preliminary group classification is rigorously defined, enhanced and related to
the theory of group classification of differential equations. Typical weaknesses in papers on
this metho...
Multiplicity and regularity of periodic solutions for a class of degenerate semilinear wave equations
Multiplicity regularity of periodic solutions class of degenerate semilinear wave equations
2011/2/28
We prove the existence of infinitely many classical periodic solutions for a class of degenerate semilinear wave equations:utt − uxx + |u|s−1u = f(x, t),for all s > 1. In particular we pro...
Asymptotic Properties of Linearized Equations of Low Compressible Fluid Motion
Asymptotic Properties of Linearized Equations Low Compressible Fluid Motion
2011/2/24
Initial–boundary value problem for linearized equations of motion of viscous barotropic fluid in a bounded domain is considered. Existence,uniqueness and estimates of weak solutions to this problem ar...
Uniqueness of normalized homeomorphic solutions to nonlinear Beltrami equations
nonlinear elliptic PDEs uniqueness of solutions quasiconformal mappings
2011/1/21
We settle the problem of the uniqueness of normalized homeomorphic solutions to nonlinear Beltrami equations @f(z) = H(z, @f(z)). It turns out that the uniqueness holds under definite and explicit bou...
Numerical Resolution near t = 0 of NonlinearEvolution Equations in the Presence of Corner Singularities in Space Dimension 1
Numerical Resolution Nonlinear Evolution Equations
2010/11/23
The incompatibilities between the initial and boundary data will cause singularities at the time-space corners, which in turn adversely affect the accuracy of the numerical schemes used to compute the...
A finite volume scheme for convection-diffusion equations with nonlinear diffusion derived from the Scharfetter-Gummel scheme
convection-diffusion equations nonlinear diffusion derived Scharfetter-Gummel scheme
2010/11/15
We propose a finite volume scheme for convection-diffusion equations with nonlinear diffusion. Such equations arise in numerous physical contexts. We will particularly focus on the drift-diffusion sy...
On fully nonlinear CR invariant equations on the Heisenberg group
nonlinear CR invariant equations Heisenberg group
2010/11/8
In this paper we provide a characterization of second order fully nonlinear CR invariant equations on the Heisenberg group, which is the analogue in the CR setting of the result proved in the Euclide...
Existence and Uniqueness of Solutions to Nonlinear Evolution Equations with Locally Monotone Operators
Nonlinear Evolution Equations Locally Monotone Operators
2010/11/9
In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical resu...
Measure valued solutions of sub-linear diffusion equations with a drift term
sublinear diffusion concentration phenomena propagation of singularities gradient flows
2010/12/9
In this paper we study nonnegative, measure valued solutions of the initial value problem for
one-dimensional drift-diffusion equations when the nonlinear diffusion is governed by an increasing C1 fu...
Preconditioners based on Windowed Fourier Frames Applied to Elliptic Partial Differential Equations
Windowed Fourier frame symbol elliptic PDE preconditioner
2010/12/3
We investigate the application of windowed Fourier frames (WFFs) to the numerical solution of partial di erential equations, focussing on elliptic equations. The action of a partial di erential operat...