Now showing items 1-15 of 15

• #### A splitting method for the nonlinear Schrödinger equation ﻿

(2011-12-31)
We introduce a splitting method for the semilinear Schrödinger equation and prove its convergence for those nonlinearities which can be handled by the classical well-posedness L2(Rd)-theory. More precisely, we prove that ...
• #### Asymptotic behaviour for fractional diffusion-convection equations ﻿

(2017-10)
We consider a convection-diffusion model with linear fractional diffusion in the sub-critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective ...
• #### Asymptotic expansions for anisotropic heat kernels ﻿

(2013-12-31)
We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lp-spaces. We mainly address two model examples. In the first one, the diffusivity ...
• #### Convergence of a two-grid algorithm for the control of the wave equation ﻿

(2009-12-31)
We analyze the problem of boundary observability of the finite-difference space semidiscretizations of the 2-d wave equation in the square.We prove the uniform (with respect to the meshsize) boundary observability for the ...
• #### Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations ﻿

(2012-12-31)
This article is devoted to the analysis of the convergence rates of several numerical approximation schemes for linear and nonlinear Schrödinger equations on the real line. Recently, the authors have introduced viscous and ...
• #### Dispersion for 1-d Schrödinger and wave equations with bv coefficients ﻿

(2016-01-01)
In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the ...
• #### Dispersion for the Schrödinger equation on networks ﻿

(2011-12-31)
In this paper, we consider the Schrödinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the solution of the linear Schrödinger ...
• #### Dispersive Properties for Discrete Schrödinger Equations ﻿

(2011-12-31)
In this paper we prove dispersive estimates for the system formed by two coupled discrete Schrödinger equations. We obtain estimates for the resolvent of the discrete operator and prove that it satisfies the limiting ...
• #### Inverse problem for the heat equation and the Schrödinger equation on a tree ﻿

(2012-12-31)
In this paper, we establish global Carleman estimates for the heat and Schrödinger equations on a network. The heat equation is considered on a general tree and the Schrödinger equation on a star-shaped tree. The Carleman ...
• #### Large-time asymptotics, vanishing viscosity and numerics for 1-D scalar conservation laws ﻿

(2014-12-31)
In this paper we analyze the large time asymptotic behavior of the discrete solutions of numerical approximation schemes for scalar hyperbolic conservation laws. We consider three monotone conservative schemes that are ...
• #### Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space ﻿

(2012-12-31)
We find lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form T(u)=-∫ ℝdK(x,y)(u(y)-u(x))dy. Here we consider a kernel K(x, y)=ψ(y-a(x))+ψ(x-a(y)) where ψ is a bounded, nonnegative ...
• #### Numerical dispersive schemes for the nonlinear Schrödinger equation ﻿

(2009-12-31)
We consider semidiscrete approximation schemes for the linear Schrödinger equation and analyze whether the classical dispersive properties of the continuous model hold for these approximations. For the conservative finite ...
• #### A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation ﻿

(2017-06-01)
In this paper we analyze the large-time behavior of the augmented Burgers equation. We first study the well-posedness of the Cauchy problem and obtain $L^1-L^p$ decay rates. The asymptotic behavior of the solution is ...
• #### A splitting method for the augmented Burgers equation ﻿

(2017-07-01)
In this paper we consider a splitting method for the augmented Burgers equation and prove that it is of ﬁrst order. We also analyze the large-time behavior of the approximated solution by obtaining the ﬁrst term in the ...
• #### Strichartz estimates for the Schrödinger equation on a tree and applications ﻿

(2010-12-31)
In this paper, we consider the Schrödinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We obtain Strichartz-like estimates for the linear semigroup and apply them to ...