Browsing by Author "Ignat, L.I."
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A splitting method for the nonlinear Schrödinger equation
Ignat, L.I. (20111231)We introduce a splitting method for the semilinear Schrödinger equation and prove its convergence for those nonlinearities which can be handled by the classical wellposedness L2(Rd)theory. More precisely, we prove that ... 
Asymptotic behaviour for fractional diffusionconvection equations
Ignat, L.I.; Stan, D. (201710)We consider a convectiondiffusion model with linear fractional diffusion in the subcritical 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
Ignat, L.I.; Zuazua, E. (20131231)We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lpspaces. We mainly address two model examples. In the first one, the diffusivity ... 
Convergence of a twogrid algorithm for the control of the wave equation
Ignat, L.I.; Zuazua, E. (20091231)We analyze the problem of boundary observability of the finitedifference space semidiscretizations of the 2d 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
Ignat, L.I.; Zuazua, E. (20121231)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 1d Schrödinger and wave equations with bv coefficients
Beli, N.; Ignat, L.I.; Zuazua, E. (20160101)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
Banica, V.; Ignat, L.I. (20111231)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
Ignat, L.I.; Stan, D. (20111231)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
Ignat, L.I.; Pazoto, A.F.; Rosier, L. (20121231)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 starshaped tree. The Carleman ... 
Largetime asymptotics, vanishing viscosity and numerics for 1D scalar conservation laws
Ignat, L.I.; Pozo, A.; Zuazua, E. (20141231)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
Ignat, L.I.; Rossi, J.D.; San Antolin, A. (20121231)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(ya(x))+ψ(xa(y)) where ψ is a bounded, nonnegative ... 
Numerical dispersive schemes for the nonlinear Schrödinger equation
Ignat, L.I.; Zuazua, E. (20091231)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 semidiscrete largetime behavior preserving scheme for the augmented Burgers equation
Ignat, L.I.; Pozo, A. (20170601)In this paper we analyze the largetime behavior of the augmented Burgers equation. We first study the wellposedness of the Cauchy problem and obtain $L^1L^p$ decay rates. The asymptotic behavior of the solution is ... 
A splitting method for the augmented Burgers equation
Ignat, L.I.; Pozo, A. (20170701)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 largetime behavior of the approximated solution by obtaining the ﬁrst term in the ... 
Strichartz estimates for the Schrödinger equation on a tree and applications
Ignat, L.I. (20101231)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 Strichartzlike estimates for the linear semigroup and apply them to ...