We study the asymptotic behavior of the solution of the Maxwell equations with a boundary condition of memory type. We consider a `Graffi' type free energy and we prove that, if the memory kernel satisfies an exponential decay condition, and the domain is strongly star shaped, then the energy of the solution exponentially decays. We also prove that the exponential decay of the kernel is a necessary condition for the exponential decay of the solution.
Exponential decay for Maxwell equations with a boundary memory condition / R., Nibbi; Polidoro, Sergio. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 302:1(2005), pp. 30-55. [10.1016/j.jmaa.2004.08.004]
Exponential decay for Maxwell equations with a boundary memory condition
POLIDORO, Sergio
2005
Abstract
We study the asymptotic behavior of the solution of the Maxwell equations with a boundary condition of memory type. We consider a `Graffi' type free energy and we prove that, if the memory kernel satisfies an exponential decay condition, and the domain is strongly star shaped, then the energy of the solution exponentially decays. We also prove that the exponential decay of the kernel is a necessary condition for the exponential decay of the solution.
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