60 citations · 83 across the 14 of their papers we have counts for
14 papers · 1 filter
Perfectly Matched Layers on Cubic Domains forPauli's Equations
Laurence Halpern, Jeffrey Rauch
This article proves the well posedness of the boundary value problemthat arises when PML algorithms are applied to Pauli's equationswith a three dimensional rectangle as computatio…
A Discrete Algorithm for General Weakly Hyperbolic Systems
Ferruccio Colombini, Tatsuo Nishitani, Jeffrey Rauch
This paper studies the Cauchy problem for variable coefficient weakly hyperbolic first order systems of partial differential operators. The hyperbolicity assumption is that for eac…
Long Time Boundedness of Planar Jump Discontinuities for Homogeneous Hyperbolic Systems
Jeffrey Rauch
Suppose that is a homogeneous constant coefficient strongly hyperbolic partial differential operator on and is a characteristic h…
Crime Pays; Homogenized Wave Equations for Long Times
Grégoire Allaire, Agnes Lamacz, Jeffrey Rauch
This article examines the accuracy for large times of asymptotic expansions from periodic homogenization of wave equations. As usual, denotes the small period of the coefficien…
Convergence along mean flows
Thomas Holding, Harsha Hutridurga, Jeffrey Rauch
We develop a technique of multiple scale asymptotic expansions along mean flows and a corresponding notion of weak multiple scale convergence. These are applied to homogenize conve…
Weakly Hyperbolic Systems by Symmetrization
F. Colombini, T. Nishitani, J. Rauch
We study hyperbolic first order systems and propose a new method proving Gevrey well posedness, constructing a symmetrizer, motivated by a special Lyapunov function for linear ODE.…
Eigenvalues for Maxwell's equations with dissipative boundary conditions
Ferruccio Colombini, Vesselin Petkov, Jeffrey Rauch
Let be the semigroup generated by Maxwell's equations in an exterior domain with dissipative boundary condition $E_{tan}- γ(…
A bound on group velocity for Bloch wave packets
Grégoire Allaire, Mariapia Palombaro, Jeffrey Rauch
This short note is a sequel to our previous papers on the asymptotic behavior of Bloch wave packet solutions of the wave equation in periodic media. The purpose is to prove that th…
Diffraction of Bloch Wave Packets for Maxwell's Equations
Grégoire Allaire, Mariapia Palombaro, Jeffrey Rauch
We study, for times of order 1/h, solutions of Maxwell's equations in an O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloc…
Global Stability of Steady Transonic Euler Shocks in Quasi-One-Dimensional Nozzles
Jeffrey Rauch, Chunjing Xie, Zhouping Xin
We prove global in time dynamical stability of steady transonic shock solutions in divergent quasi-one-dimensional nozzles. We assume neither the smallness of the relative slope of…
Optimal Focusing for Monochromatic Scalar and Electromagnetic Waves
Jeffrey Rauch
For monochromatic solutions of D'Alembert's wave equation and Maxwell's equations, we obtain sharp bounds on the sup norm as a function of the far field energy. The extremizer in t…
Stability of Transonic Shock Solutions for One-Dimensional Euler-Poisson Equations
Tao Luo, Jeffrey Rauch, Chunjing Xie +1
In this paper, both structural and dynamical stabilities of steady transonic shock solutions for one-dimensional Euler-Poission system are investigated. First, a steady transonic s…
Dispersive Stabilization
Guy Metivier, Jeffrey Rauch
Ill posed linear and nonlinear initial value problems may be stabilized, that it converted to to well posed initial value problems, by the addition of purely nonscalar linear dispe…
Focusing of Spherical Nonlinear Pulses in , III. Sub and Supercritical cases
Remi Carles, Jeffrey Rauch
We study the validity of geometric optics in for nonlinear wave equations in three space dimensions whose solutions, pulse like, focus at a point. If the amplitude of th…