Action Principles for Electromagnetism,
POLITECNICO DI MILANO (ITALY) ISTITUTO DI MATEMATICA
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The possibility of a variational formulation for linear initial value problems, discovered by Gurtin, has been recently discussed in detail by Tonti, who put in evidence the importance of a convolution bilinear form for the existence of such a variational formulation. In particular, using a convolution bilinear form, one can give a variational formulation for linear initial value problems in a way that greatly simplifies the Gurtin method. The purpose of the paper is to apply the convolution bilinear form to the variational formulation of the boundary-initial value problem of the electromagnetic field. An analysis of the operator features of this problem is made, and a variational formulation is given, simpler than the one obtained with the Gurtin method.
- Electricity and Magnetism