Equations of Maxwell type
Copyright policy )Equations of Maxwell type
For an elliptic complex of first order differential operators on a smooth manifold, we define a system of two equations which can be thought of as abstract Maxwell equations. The formal theory of this system proves to be very similar to that of classical Maxwell's equations. The paper focuses on boundary value problems for the abstract Maxwell equations, especially on the Cauchy problem.
17 pages, 1 figure
- UNIVERSITAET POTSDAM Germany
- University of Potsdam Germany
- Samarkand State University Uzbekistan
Stratton–Chu formulas, Scattering, Mathematics - Analysis of PDEs, Green formulas, 35Q60, FOS: Mathematics, electromagnetic waves, Stratton-Chu formulas, Cauchy problem, Electromagnetic waves, Hyperbolic equations on manifolds, elliptic complex, Applied Mathematics, scattering, Institut für Physik und Astronomie, Fundamental solutions to PDEs, 35Cxx, Maxwell equations, Electromagnetic theory (general), Elliptic complex, Other special methods applied to PDEs, 35Q60; 35Cxx, Analysis, Analysis of PDEs (math.AP)
Stratton–Chu formulas, Scattering, Mathematics - Analysis of PDEs, Green formulas, 35Q60, FOS: Mathematics, electromagnetic waves, Stratton-Chu formulas, Cauchy problem, Electromagnetic waves, Hyperbolic equations on manifolds, elliptic complex, Applied Mathematics, scattering, Institut für Physik und Astronomie, Fundamental solutions to PDEs, 35Cxx, Maxwell equations, Electromagnetic theory (general), Elliptic complex, Other special methods applied to PDEs, 35Q60; 35Cxx, Analysis, Analysis of PDEs (math.AP)
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