Transportic equations of Maxwell, their fundamental and generalized solutions at constant speed of moving emitters
L.A. Alexeyeva1, I. A. Kanymgaziyeva2
1Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
2L.N.Gumilyov Eurasian National University, Astana, Kazakhstan
Email: alexeeva47@mail.ru
The article discusses transport solutions of the system of Maxwell's equations under the action of mobile sources of electromagnetic waves moving at a constant speed in a fixed direction. Fundamental and generalized solutions have been constructed for speeds of motion less than the speed of light in the medium, and their regular representation in analytical form. To do this, in the space of Fourier transformftion over coordinates and time, the Green's tensor has been constructed. To restore the originals, the fundamental solutions of the wave equation and properties of Fourier transformation were used. Construction of solutions for arbitrary moving sourthes are based on the property of convolution of fundamental solutions differential equations with right-hand side. Formulas are given for calculating the electric and magnetic intensities for moving emitters of various types, useful for radiodetechnical applications. Keywords: light speed, speed of movement, Mach number, Green's tensor, generalized solutions, electromagnetic waves, radio waves.
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