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Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations
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 ...
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 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 ...
Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space
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 ...