Physical description 
1 online resource (ix, 458 pages) : illustrations. 
Series 
Applied Mathematical Sciences, 00665452 ; 198


Applied mathematical sciences (SpringerVerlag New York Inc.) ; 198. 00665452


Springer Mathematics and Statistics eBooks 2018 English+International

Contents 
Foreword  Physical framework and models  Electromagnetic fields and Maxwell's equations  Stationary equations  Coupling with other models  Approximate models  Elements of mathematical classifications  Boundary conditions and radiation conditions  Energy matters  Bibliographical notes  Basic applied functional analysis  Function spaces for scalar fields  Vector fields: standard function spaces  Practical function spaces in the (t, x) variable  Complements of applied functional analysis  Vector fields: tangential trace revisited  Scalar and vector potentials: the analyst's and topologist's points of view  Extraction of scalar potentials and consequences  Extraction of vector potentials  Extraction of vector potentials  Vanishing normal trace  Extraction of vector potentials  Complements  Helmholtz decompositions  Abstract mathematical framework  Basic Results  Static problems  Timedependent problems  Timedependent problems: improved regularity results  Timeharmonic problems  Summing up  Analyses of exact problems: firstorder models  Energy matters: uniqueness of the fields  Wellposedness  Analyses of approximate models  Electrostatic problem  Magnetostatic problem  Further comments around static problems  Other approximate models  Analyses of exact problems: secondorder models  Firstorder to secondorder equations  Wellposedness of the secondorder Maxwell equations  Secondorder to firstorder equations  Other variational formulations  Compact imbeddings  Improved regularity for augmented and mixed augmented formulations  Analyses of timeharmonic problems  Compact imbeddings: complements  Free vibrations in a domain encased in a cavity  Sustained vibrations  Interface problem between a dielectric and a Lorentz material  Comments  Dimensionally reduced models: derivation and analyses  Twoandahalf dimensional (2 1/2 2D) models  Twodimensional (2D) models  Some results of functional analysis  Existence and uniqueness results (2D problems)  Analyses of coupled models  The VlasovMaxwell and VlasovPoisson systems  Magnetohydrodynamics  References  Index of function spaces  Basic Spaces  Electromagnetic spaces  Dimension reduction and weighted spaces  Spaces measuring time regularity  List of Figures  Index. 
Bibliography 
Includes bibliographical references and index. 
Summary 
This book presents an indepth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to wellposedness results and the coupled models of plasma physics (VlasovMaxwell and VlasovPoisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to wellposedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasistatic problems, timeharmonic problems (including fixed frequency or Helmholtzlike problems and unknown frequency or eigenvalue problems), and timedependent problems, with or without constraints. They are then applied to prove the wellposedness 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 VlasovPoisson, VlasovMaxwell 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 doctoratelevel courses on mathematical electromagnetism as it requires only a bachelorlevel knowledge of analysis. 
Other author 
Ciarlet, Patrick, author.


Labrunie, Simon, author.


SpringerLink issuing body.

Subject 
Electromagnetism  Mathematics.


Electromagnetism  Data processing.


Electromagnetism  Mathematical models.


Electronic books. 
ISBN 
9783319708423 

3319708422 

9783319708416 

3319708414 

3319708414 

9783319708416 
Standard Number 
10.1007/9783319708423 

9783319708416 
