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A nonlocal convection–diffusion equation
In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut=J∗u−u+G∗(f(u))−f(u) in Rd, with J radially symmetric and G not necessarily symmetric. First, weExpand
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Numerical Dispersive Schemes for the Nonlinear Schrödinger Equation
TLDR
We consider semidiscrete approximation schemes for the linear Schrodinger equation and analyze whether the classical dispersive properties of the continuous model hold for these approximations. Expand
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A splitting method for the nonlinear Schrödinger equation
Abstract We introduce a splitting method for the semilinear Schrodinger equation and prove its convergence for those nonlinearities which can be handled by the classical well-posedness L 2 ( R d )Expand
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Decay estimates for nonlocal problems via energy methods
Abstract In this paper we study the applicability of energy methods to obtain bounds for the asymptotic decay of solutions to nonlocal diffusion problems. With these energy methods we can deal withExpand
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Inverse problem for the heat equation and the Schrödinger equation on a tree
In this paper, we establish global Carleman estimates for the heat and Schrodinger equations on a network. The heat equation is considered on a general tree and the Schrodinger equation on aExpand
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Refined asymptotic expansions for nonlocal diffusion equations
Abstract.We study the asymptotic behavior for solutions to nonlocal diffusion models of the form ut = J * u – u in the whole $${\mathbb{R}}^d$$ with an initial condition u(x, 0) = u0(x). UnderExpand
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Large-time asymptotics, vanishing viscosity and numerics for 1-D scalar conservation laws
TLDR
We analyze the large time asymptotic behavior of the discrete solutions of numerical approximation schemes for scalar hyperbolic conservation laws that are consistent with the one-sided Lipschitz condition. Expand
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Dispersive properties of a viscous numerical scheme for the Schrodinger equation Proprietes dispersives d'un schema numer´ique visqueux pour l'´equation de Schrodinger
In this work we study the dispersive properties of the numerical approximation schemes for the free Schrodinger equation. We consider finite-dierence space semi-discretizations. We first show thatExpand
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[The evaluation of sound level in dental practice].
Noise pollution is one of the most important problems of the contemporary world. Dentistry is one of the most affected areas because the activity in a dental practice involves the use of differentExpand
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Convergence of a two-grid algorithm for the control of the wave equation
We analyze the problem of boundary observability of the finite-difference space semi-discretizations of the 2-d wave equation in the square. We prove the uniform (with respect to the mesh-size)Expand
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