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The initial boundary value problem for the Schröudinger equation

✍ Scribed by Leif Abrahamsson; Heinz-Otto Kreiss

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
243 KB
Volume
13
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We study the stability properties of the one‐dimensional Schrödinger equation with boundary conditions that involve the derivative in the direction of propagation (or time). We show that this type of boundary condition might cause a strong growth of the amplitude of the solution. Such a model is not useful for numerical computations. One example is the parabolic wave equation in underwater acoustics for wave propagation in a downsloping duct with the normal derivative condition ∂u/∂n =0 at the bottom.

📜 SIMILAR VOLUMES

An Initial Boundary Value Problem for Pa
An Initial Boundary Value Problem for Parabolic Differential-Operator Equations
✍ Sasun Yakubov 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 143 KB

In this paper we give, for the first time, an abstract interpretation of such initial boundary value problems for parabolic equations that a part of boundary value conditions contains also a differentiation on the time t. Initial boundary value problems for parabolic equations are reduced to the Cau