Interface Problems for Dispersive Equations
نویسندگان
چکیده
منابع مشابه
Interface Problems for Dispersive equations
The interface problem for the linear Schrödinger equation in one-dimensional piecewise homogeneous domains is examined by providing an explicit solution in each domain. The location of the interfaces is known and the continuity of the wave function and a jump in their derivative at the interface are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-siz...
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Non homogeneous boundary value problems for linear dispersive equations
While the non-homogeneous boundary value problem for elliptic, hyperbolic and parabolic equations is relatively well understood, there are still few results for general dispersive equations. We define here a convenient class of equations comprising the Schrödinger equation, the Airy equation and linear ‘Boussinesq type’ systems, which is in some sense a generalization of strictly hyperbolic equ...
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We introduce a new dispersion-velocity particle method for approximating solutions of linear and nonlinear dispersive equations. This is the first time in which particle methods are being used for solving such equations. Our method is based on an extension of the diffusion-velocity method of Degond and Mustieles (SIAM J. Sci. Stat. Comput. 11(2), 293 (1990)) to the dispersive framework. The mai...
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These notes were written as a guideline for a short talk; hence, the references and the statements of the theorems are often not given in full details. The point of these notes is to summarize the different directions that the study of dispersive equations has taken in the last ten years. I would like to mention here a few recent textbooks that treat different parts of this subject. They could ...
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ژورنال
عنوان ژورنال: Studies in Applied Mathematics
سال: 2014
ISSN: 0022-2526
DOI: 10.1111/sapm.12070