Dirichlet and Neumann problems for Klein-Gordon-Maxwell systems
Pietro d'Avenia, Lorenzo Pisani, Gaetano Siciliano
TL;DR
This paper investigates the existence of standing wave solutions with electrostatic fields for the Klein-Gordon-Maxwell system in bounded domains, under specific boundary conditions on matter and electric potential.
Contribution
It provides new results on the existence of solutions with prescribed boundary conditions for the Klein-Gordon-Maxwell system in bounded domains.
Findings
Existence of standing wave solutions with Dirichlet boundary conditions on matter field.
Existence of solutions with either Dirichlet or Neumann boundary conditions on electric potential.
Analysis of solutions in a bounded spatial domain for the Klein-Gordon-Maxwell system.
Abstract
This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet boundary conditions on the matter field, and either Dirichlet or Neumann boundary conditions on the electric potential.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Geometric Analysis and Curvature Flows