Hidden Bibliographic Details
| Other authors / contributors: | Ciarlet, Patrick, author.
Labrunie, Simon, author.
|
|---|
| ISBN: | 9783319708423
3319708422
3319708414
9783319708416
9783319708430
3319708430
9783030099978
3030099970
9783319708416
3319708414
|
|---|
| Digital file characteristics: | text file PDF
|
|---|
| Notes: | Includes bibliographical references and index.
|
|---|
| Summary: | 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.
|
|---|
| Other form: | Printed edition: 9783319708416
|
|---|
| Standard no.: | 10.1007/978-3-319-70842-3
9783319708416
10.1007/978-3-319-70
|
|---|
