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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Space-time finite and boundary element methods for the wave equation
波动方程 时空有限元 边界元方法
2023/4/21
In this talk we will review some recent results on space-time finite and boundary element methods for the wave equation. As a first model problem we consider the inhomogeneous wave equation with zero ...
FAST MULTISCALE GAUSSIAN WAVEPACKET TRANSFORMS AND MULTISCALE GAUSSIAN BEAMS FOR THE WAVE EQUATION
ast multiscale Gaussian wavepacket transforms multiscale Gaussian beams wave equations
2015/7/14
We introduce a new multiscale Gaussian beam method for the numerical solution of the wave equation with smooth variable coefficients. The first computational question addressed in this paper is how to...
A Convergent Multiscale Gaussian-Beam Parametrix for the Wave Equation
Multiscale Gaussian beams Multiscale Gaussian wave packets Phase space transform Wave equations
2015/7/14
The Gaussian beam method is an asymptotic method for wave equations with highly oscillatory data. In a recent published paper by two of the authors, a multiscale Gaussian beam method was first propose...
Asymptotics of the solutions of the stochastic lattice wave equation
solutions stochastic lattice wave equation
2015/7/14
We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-...
The shifted wave equation on Damek--Ricci spaces and on homogeneous trees
Abel transform Damek–Ricci space homogeneous tree Huygens’ principle hyperbolic space wave equation wave propagation
2012/6/27
We solve explicitly the shifted wave equation on Damek--Ricci spaces, using Asgeirsson's theorem and the inverse dual Abel transform. As an application, we investigate Huygens' principle. A similar an...
Inversion of circular means and the wave equation on general planar domains
Inversion of circular equation general planar domains Analysis of PDEs
2012/6/25
We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on an arbitrarily shaped bounded domain $\Omega \subset \R^2$. As a main result we ...
Existence and exponential stability of a damped wave equation with dynamic boundary conditions and a delay term
Damped wave equations boundary delay global solutions exponential stability Kelvin-Voigt damping dynamic boundary conditions
2012/6/21
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions related to the Kelvin-Voigt damping and a delay term acting on the boundary. If the weight of the delay ter...
Asymptotics of the critical non-linear wave equation for a class of non star-shaped obstacles
Asymptotics the critical non-linear wave equation non star-shaped obstacles Analysis of PDEs
2012/6/14
Scattering for the energy critical non-linear wave equation for domains exterior to non trapping obstacles in 3+1 dimension is known for the star-shaped case. In this paper, we extend the scattering f...
Classification of radial solutions of the focusing, energy-critical wave equation
Classification radial solutions focusing energy-critical wave equation Analysis of PDEs
2012/4/17
In this paper, we describe the asymptotic behaviour of globally defined solutions and of bounded solutions blowing up in finite time of the radial energy-critical focusing non-linear wave equation in ...
Improved local energy decay for the wave equation on asymptotically Euclidean odd dimensional manifolds in the short range case
Local energy decay resolvent smoothness wave equation odd dimensions low frequencies asymptotically Euclidean manifolds
2011/9/21
Abstract: We show improved local energy decay for the wave equation on asymptotically Euclidean manifolds in odd dimensions in the short range case. The precise decay rate depends on the decay of the ...
A decay estimate for a wave equation with trapping and a complex potential
wave equation decay estimate complex potential Analysis of PDEs
2011/9/19
Abstract: In this brief note, we consider a wave equation that has both trapping and a complex potential. For this problem, we prove a uniform bound on the energy and a Morawetz (or integrated local e...
The blow-up theorem of a discrete semilinear wave equation
The blow-up theorem semilinear wave equation Analysis of PDEs
2011/9/1
Abstract: In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equa...
Global attractors for the one dimensional wave equation with displacement dependent damping
Attractors wave equations
2011/2/24
We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly
positive near the o...
Numerical solution of regularized long wave equation by reduced differential transform method
Reduced differential transform method Adomian decomposition method Variational iteration method
2010/9/25
In this paper, a general framework of the reduced differential transform method is presented for solving the regularized long wave (RLW) equation. In this method, the solution is calculated in the for...
Exponential fitting of the damped wave equation
damped wave equation exponential fitting stability analysis
2010/9/26
Herein, the Control Region Approximation [1, 2] is applied to the damped wave equation both with and without exponential fitting [3]. It is shown that exponential fitting is advantageous as regards th...