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New variational principles for systems of partial differential equations


Myers, John Richard (1972) New variational principles for systems of partial differential equations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/X8KY-4K24.


The question of finding variational principles for coupled systems of first order partial differential equations is considered. Using a potential representation for solutions of the first order system a higher order system is obtained. Existence of a variational principle follows if the original system can be transformed to a self-adjoint higher order system. Existence of variational principles for all linear wave equations with constant coefficients having real dispersion relations is established. The method of adjoining some of the equations of the original system to a suitable Lagrangian function by the method of Lagrange multipliers is used to construct new variational principles for a class of linear systems. The equations used as side conditions must satisfy highly-restrictive integrability conditions. In the more difficult nonlinear case the system of two equations in two independent variables can be analyzed completely. For systems determined by two conservation laws the side condition must be a conservation law in addition to satisfying the integrability conditions.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Whitham, Gerald Beresford
Thesis Committee:
  • Unknown, Unknown
Defense Date:22 May 1972
Record Number:CaltechTHESIS:03292013-092331028
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7563
Deposited On:29 Mar 2013 18:15
Last Modified:09 Nov 2022 19:20

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