Mostrando recursos 1 - 20 de 238

  1. A stability result for solitary waves in nonlinear dispersive equations

    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.

  2. On the finite time blow-up of the Euler-Poisson equations in $\Bbb R^{2}$

    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.

  3. Circulation of car traffic in congested urban areas

    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...

  4. Global classical solutions of the Vlasov-Darwin system for small initial data

    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.

  5. On selection dynamics for continuous structured populations

    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).

  6. Existence of axially symmetric solutions to the Vlasov-Poisson system depending on Jacobi's integral

    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.

  7. An analysis of the Darwin model of approximation to Maxwell?s equations in 3-D unbounded domains

    Liao, Caixiu; Ying, Lung-An

  8. A higher order numerical method for 3-d double periodic electromagnetic scattering problem

    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...

  9. The linearization of a boundary value problem for a scalar conservation law

    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.

  10. A nonlinear test model for filtering slow-fast systems

    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...

  11. Global solutions to the Einstein equations with cosmological constant on the Friedman-Robertson-Walker space times with plane, hyperbolic, and spherical symmetries

    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.

  12. Second-order slope limiters for the simultaneous linear advection of (not so) independent variables

    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.

  13. The derivatives of Asian call option prices

    Choi, Jungmin; Kim, Kyounghee

  14. A simple Eulerian finite-volume method for compressible fluids in domains with moving boundaries

    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]...

  15. The drift-flux asymptotic limit of barotropic two-phase two-pressure models

    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.

  16. Perron-Frobenius theorem for nonnegative tensors

    Chang, K. C.; Pearson, K.; Zhang, T.
    We generalize the Perron–Frobenius Theorem for nonnegative matrices to the class of nonnegative tensors.

  17. Global existence of solutions to the Einstein equations with cosmological constant for a perfect relativistic fluid on a Blanchi type-I space-time

    Noutchegeume, N.; Gadjou Tamghe, L. R.
    Global existence is proved in the case of positive cosmological constant, and asymptotic behavior is investigated.

  18. On the Bakry-Emery criterion for linear diffusions and weighted porous media equations

    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...

  19. Superpositions and higher order Gaussian beams

    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...

  20. The parabolic-parabolic Keller-Segel model in R2

    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.

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