A minimum variational approach is developed for Maxwell's equations. The existence and uniqueness of strong solutions is shown to be equivalent to the existence of a point of strict minimum for an appropriate functional, using some thermodynamical restrictions on the constitutive equations. One of Maxwell's equations is treated as a constraint in defining the domain of such a functional. Suitable functionals are constructed for several cases.
Bosello C.A., Nibbi R. (1999). A principle of constrained minimum in electromagnetism. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 37(2), 253-268 [10.1016/s0020-7225(98)00060-3].
A principle of constrained minimum in electromagnetism
Bosello C. A.;Nibbi R.
1999
Abstract
A minimum variational approach is developed for Maxwell's equations. The existence and uniqueness of strong solutions is shown to be equivalent to the existence of a point of strict minimum for an appropriate functional, using some thermodynamical restrictions on the constitutive equations. One of Maxwell's equations is treated as a constraint in defining the domain of such a functional. Suitable functionals are constructed for several cases.File in questo prodotto:
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