# American Institute of Mathematical Sciences

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Global classical solutions for the "One and one-half'' dimensional relativistic Vlasov-Maxwell-Fokker-Planck system
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March  2015, 8(1): 153-168. doi: 10.3934/krm.2015.8.153

## Global magnetic confinement for the 1.5D Vlasov-Maxwell system

 1 Department of Mathematics, Pennsylvania State University, State College, PA 16802, United States 2 Department of Mathematics, The University of Akron, Akron, OH 44325, United States 3 Brown University, Department of Mathematics and Lefschetz Center for Dynamical Systems, Providence, RI 02912

Received  August 2014 Revised  September 2014 Published  December 2014

We establish the global-in-time existence and uniqueness of classical solutions to the one and one-half'' dimensional relativistic Vlasov--Maxwell systems in a bounded interval, subject to an external magnetic field which is infinitely large at the spatial boundary. We prove that the large external magnetic field confines the particles to a compact set away from the boundary. This excludes the known singularities that typically occur due to particles that repeatedly bounce off the boundary. In addition to the confinement, we follow the techniques introduced by Glassey and Schaeffer, who studied the Cauchy problem without boundaries.
Citation: Toan T. Nguyen, Truyen V. Nguyen, Walter A. Strauss. Global magnetic confinement for the 1.5D Vlasov-Maxwell system. Kinetic & Related Models, 2015, 8 (1) : 153-168. doi: 10.3934/krm.2015.8.153
##### References:

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##### References:
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