Recursos de colección
Akers, Benjamin; Milewski, Paul A.
The stability of solitary traveling waves in a general class of conservative nonlinear
dispersive equations is discussed. A necessary condition for the exchange of stability of traveling
waves is presented; an unstable eigenmode may bifurcate from the neutral translational mode only
at relative extrema of the wave energy. This paper extends a result from Hamiltonian systems, and
from a few integrable partial differential equations, to a broader class of conservative differential
equations, with particular application to gravity-capillary surface waves.
Chae, Donghao; Tadmor, Eitan
We prove the finite time blow-up for $C^1$ solutions of the attractive Euler-Poisson
equations in $\Bbb R^{2}$, $n\geq1$, with and without background state, for a large set of ’generic’ initial data. We
characterize this supercritical set by tracing the spectral dynamics of the deformation and vorticity
tensors.
Cascone, Annunziata; D'Apice, Ciro; Piccoli, Benedetto; Rarità, Luigi
The aim of this work is to understand how urban traffic behavior, especially in cases
of congestion, can be improved by an accurate choice of traffic coefficients. For this, we define three
cost functionals that measure average velocity, average travelling time and total flux of cars. The
global optimal control problem for a complex network is difficult to solve both from analytical and
numerical points of view. Thus, we focus on a simple junction with one incoming road and two
outgoing roads (junctions of 1×2 type), obtaining exact solutions to a simple optimization problem.
Then, we use such results at each node of the network. The...
Seehafer, Martin
A global-in-time existence theorem for classical solutions of the Vlasov-Darwin sys-
tem is given under the assumption of smallness of the initial data. Furthermore it is shown that in
case of spherical symmetry the system degenerates to the relativistic Vlasov-Poisson system.
Desvillettes, Laurent; Jabin, Pierre Emmanuel; Mischler, Stéphane; Raoul, Gaël
In this paper, we provide results about the long time behavior of integrodifferential
equations appearing in the study of populations structured with respect to a quantitative (continuous)
trait, which are submitted to selection (or competition).
Schulze, Achim
We prove the existence of axially symmetric solutions to the Vlasov–Poisson
system in a rotating setting for sufficiently small angular velocity. The
constructed steady states depend on Jacobi’s integral and the proof relies
on an implicit function theorem for operators.
Liao, Caixiu; Ying, Lung-An
Nicholas, Michael J.
We develop a method for 3D doubly periodic electromagnetic scattering. We
adapt the Müller integral equation formulation of Maxwell's equations to
the periodic problem, since it is a Fredholm equation of the second kind. We
use Ewald splitting to efficiently calculate the periodic Green's functions.
The approach is to regularize the singular Green's functions and to compute
integrals with a trapezoidal sum. Through asymptotic analysis near the
singular point, we are able to identify the largest part of the smoothing
error and to subtract it out. The result is a method that is third order in
the grid spacing size. We present results for various scatterers, including
a test...
Caetano, Filipa
The aim of this paper is to study a boundary value problem for a linear
scalar equation with discontinuous coefficients. This kind of problem
appears in the framework of the analysis of the linearized stability of a
fluid flow with respect to small perturbations of the boundary data. The
linear equation that we are interested in is obtained by linearizing the
equations which govern the flow, and involves discontinuous coefficients and
nontrivial products. We present a direct approach based on the one
introduced by Godlewski and Raviart, which leads to measure solutions, gives
a sense of these nontrivial products, and yields simple numerical schemes
that give good results.
Gershgorin, Boris; Majda, Andrew
A nonlinear test model for filtering turbulent signals from partial
observations of nonlinear slow-fast systems with multiple time scales is
developed here. This model is a nonlinear stochastic real triad model with
one slow mode, two fast modes, and catalytic nonlinear interaction of the
fast modes depending on the slow mode. Despite the nonlinear and
non-Gaussian features of the model, exact solution formulas are developed
here for the mean and covariance. These formulas are utilized to develop a
suite of statistically exact extended Kalman filters for the slow-fast
system. Important practical issues such as filter performance with partial
observations, which mix the slow and fast modes, model errors through...
Noutchegueme, Norbert; Chendjou, Gilbert
Global existence of solutions is proved, in the case of a positive
cosmological constant and positive initial velocity of the cosmological
expansion factor on the three types of Friedman- Robertson-Walker
space-time, and asymptotic behavior is investigated.
Tran, Quang Huym
We propose a strategy to perform second-order enhancement using
slope-limiters for the simultaneous linear advection of several scalar
variables. Our strategy ensures a discrete min-max principle not only for
each variable but also for any number of non-trivial combinations of them,
which represent control variables. This problem arises in fluid
mechanics codes using the Arbitrary Lagrange-Euler formalism, where the
additional monotonicity property on control variables is required by
physical considerations within the remap step.
Choi, Jungmin; Kim, Kyounghee
Chertock, Alina; Kurganov, Alexander
We introduce a simple new Eulerian method for treatment of moving boundaries
in compressible fluid computations. Our approach is based on the extension
of the interface tracking method recently introduced in the context of
multifluids. The fluid domain is placed in a rectangular computational
domain of a fixed size, which is divided into Cartesian cells. At every
discrete time level, there are three types of cells: internal, boundary, and
external ones. The numerical solution is evolved in internal cells only. The
numerical fluxes at the cells near the boundary are computed using the
technique from [A. Chertock, S. Karni and A. Kurganov, M2AN Math. Model.
Numer. Anal., to appear]...
Ambroso, A.; Chalons, C.; Coquel, F.; Galié, T.; Godlewski, E.; Raviart, P. A.; Seguin, N.
We study the asymptotic behavior of the solutions of barotropic two-phase two-pressure models, with pressure relaxation, drag force and external forces. Using Chapman-Enskog expansions close to the expected equilibrium, a drift-flux model with a Darcy type closure law is obtained. Also, restricting this closure law to permanent flows (defined as steady flows in some Lagrangian frame), we can obtain a drift-flux model with an algebraic closure law, in the spirit of Zuber-Findlay models. The example of a two-phase flow in a vertical pipe is described.
Chang, K. C.; Pearson, K.; Zhang, T.
We generalize the Perron–Frobenius Theorem for nonnegative matrices to the class of nonnegative tensors.
Noutchegeume, N.; Gadjou Tamghe, L. R.
Global existence is proved in the case of positive cosmological constant, and asymptotic behavior is investigated.
Dolbeault, J.; Nazaret, B.; Savare, G.
The goal of this paper is to give a non-local sufficient condition for generalized Poincaré inequalities which extends the well-known Bakry-Emery condition. Such generalized Poincaré inequalities have been introduced by W. Beckner in the Gaussian case and provide, along the Ornstein-Uhlenbeck flow, the exponential decay of some generalized entropies which interpolate between the L2 norm and the usual entropy. Our criterion improves on results which, for instance, can be deduced from the Bakry-Emery criterion and Holley-Stroock type perturbation results. In a second step, we apply the same strategy to non-linear equations of porous media type. This provides new interpolation inequalities...
Tanushev, N. M.
High frequency solutions to partial differential equations (PDEs) are notoriously
difficult to simulate numerically due to the large number of grid points required to resolve the wave
oscillations. In applications, one often must rely on approximate solution methods to describe the
wave field in this regime. Gaussian beams are asymptotically valid high frequency solutions concen-
trated on a single curve through the domain. We show that one can form integral superpositions of
such Gaussian beams to generate more general high frequency solutions to PDEs.
¶ As a particular example, we look at high frequency solutions to the constant coefficient wave
equation and construct Gaussian beam solutions with...
Calvez, V.; Corrias, L.
This paper is devoted mainly to the global existence problem for the two-dimensional
parabolic-parabolic Keller-Segel system in the full space. We derive a critical mass threshold below
which global existence is ensured. Carefully using energy methods and ad hoc functional inequalities,
we improve and extend previous results in this direction. The given threshold is thought to be the
optimal criterion, but this question is still open. This global existence result is accompanied by a
detailed discussion on the duality between the Onofri and the logarithmic Hardy-Littlewood-Sobolev
inequalities that underlie the following approach.