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arXiv · 1407.5712

Lagrangian Variational Framework for Boundary Value Problems

Alexander Figotin·Guillermo Reyes
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Abstract

A boundary value problem is commonly associated with constraints imposed on a system at its boundary. We advance here an alternative point of view treating the system as interacting "boundary" and "interior" subsystems. This view is implemented through a Lagrangian framework that allows to account for (i) a variety of forces including dissipative acting at the boundary; (ii) a multitude of features of interactions between the boundary and the interior fields when the boundary fields may differ from the boundary limit of the interior fields; (iii) detailed pictures of the energy distribution and its flow; (iv) linear and nonlinear effects. We provide a number of elucidating examples of the structured boundary and its interactions with the system interior. We also show that the proposed approach covers the well known boundary value problems.

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Alexander Figotin, Guillermo Reyes. 2014-07-22. Lagrangian Variational Framework for Boundary Value Problems. https://doi.org/10.1063/1.4931135

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