1. Dispersion for the Schrödinger equation on networks
- Author
-
Valeria Banica and Liviu I. Ignat
- Subjects
Partial differential equation ,Differential equation ,010102 general mathematics ,Mathematical analysis ,Characteristic equation ,Statistical and Nonlinear Physics ,Kadomtsev–Petviashvili equation ,01 natural sciences ,Burgers' equation ,010101 applied mathematics ,symbols.namesake ,Integro-differential equation ,symbols ,Riccati equation ,0101 mathematics ,Nonlinear Schrödinger equation ,Mathematical Physics ,Mathematics - Abstract
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 equation with constant coefficients. This allows us to prove dispersive estimates, which in turn are useful for solving the nonlinear Schrödinger equation. The proof extends also to the laminar case of positive step-function coefficients having a finite number of discontinuities.
- Published
- 2011
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