Advances in Differential Equations

Derivation and physical interpretation of general boundary conditions

Gisèle Ruiz Goldstein

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Abstract

In this paper we give new derivations of the heat and wave equation which incorporate the boundary conditions into the formulation of the problems. The principle of least action and the inclusion of a kinetic energy contribution on the boundary are used to derive the wave equation together with kinetic boundary conditions. The methods described for both equations admit all of the standard boundary conditions as well as general Wentzell and dynamic boundary conditions; in addition the boundary conditions arise naturally as part of the formulation of the problems. The physical interpretation for general Wentzell boundary conditions is given for both the heat and wave equations.

Article information

Source
Adv. Differential Equations Volume 11, Number 4 (2006), 457-480.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867704

Mathematical Reviews number (MathSciNet)
MR2215623

Zentralblatt MATH identifier
1107.35010

Subjects
Primary: 35K20: Initial-boundary value problems for second-order parabolic equations
Secondary: 35K60: Nonlinear initial value problems for linear parabolic equations 35L20: Initial-boundary value problems for second-order hyperbolic equations 35L70: Nonlinear second-order hyperbolic equations

Citation

Goldstein, Gisèle Ruiz. Derivation and physical interpretation of general boundary conditions. Adv. Differential Equations 11 (2006), no. 4, 457--480. https://projecteuclid.org/euclid.ade/1355867704.


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