Leseprobe
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Mathematical Foundations of Computational Electromagnetism
Patrick Ciarlet, Simon Labrunie, Franck Assous, et al.
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Springer International Publishing 
Naturwissenschaften, Medizin, Informatik, Technik / Theoretische Physik
Beschreibung
This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations.
The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.
Kundenbewertungen
linear Vlasov equation, electromagnetic Darwin model, magnetostatic field problem, Magnetohydrodynamics, time harmonic electromagnetic fields, Vlasov Maxwell equation, electrostatic problem, Vlasov Maxwell model, Vlasov Poisson equation, Vlasov Maxwell system, Maxwell equations, Vlasov Poisson systems, magnetostatics, Helmholtz decomposition