Lagrangian variational framework for boundary value problems
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; and (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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 01, 2015
- Source ID
- 10.1063/1.4931135
Entities
People
- Alexander Figotin
- Guillermo Reyes
Organizations
- Air Force Office of Scientific Research
- University of California, Irvine