A Note on a General Linear Initial-Boundary Value Problem

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Abstract
The methods of time convolutions and the Laplace transform are used to derive a variational principle, reciprocity principle and uniqueness theorem for a general linear initial-boundary value problem. The formulation includes as special cases the initial-boundary value problems associated with electromagnetism (telegraphy equation), nuclear physics (neutron diffusion equation), quantum mechanics (Klein-Gordon equation) and elasticity theory, classical wave propagation (wave equation), heat conduction and diffusion (heat equation).

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