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Asymptotic stability for a non‐local problem in electromagnetism
Author(s) -
Bosello Carlo Alberto
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19990925)22:14<1189::aid-mma72>3.0.co;2-f
Subject(s) - mathematics , uniqueness , maxwell's equations , boundary value problem , mathematical analysis , electromagnetism , a priori estimate , domain (mathematical analysis) , exponential stability , stability (learning theory) , nonlinear system , physics , quantum mechanics , machine learning , computer science
In this paper, constitutive equations of non‐local type are coupled with Maxwell equations and the resulting differential problem is studied. A weak formulation is given for an initial–boundary‐value problem for Maxwell equations in a medium obeying such constitutive equations with perfectly conducting boundary, and it is shown that such a problem admits at most one solution. The uniqueness theorem is then shown to imply the density of the range of a certain operator in the space of solutions and this result, together with an a priori energy inequality, is used to prove existence of solutions. Then the study of asymptotic stability of solutions is addressed. In particular, solutions are shown to be L 2 in time over (0,∞). Finally, a brief description is given of the alternative problem arising when more general constitutive equations are used. Copyright © 1999 John Wiley & Sons, Ltd.