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Cauchy problems for the generalized system of Maxwell's equations

by Komil Olimdzhanovich Mahmudov

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A mathematical treatment of generalized Maxwell-type Cauchy problems

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A mathematical treatment of generalized Maxwell-type Cauchy problems

This 100-page monograph examines ill-posed Cauchy problems for Maxwell-type elliptic systems in bounded regions and in n-dimensional space. It develops several analytical components: a matrix left fundamental solution for a special class of electrodynamics equations, a generalized Stratton-Chu formula, solvability conditions, and a Carleman formula. The construction of that formula uses bases with double orthogonality and is presented as an explicit means of restoring solutions to the generalized Maxwell system within a bounded domain. The emphasis is on the mathematical structure and solution theory of generalized electrodynamics equations rather than on applied electromagnetic engineering.

Good fit for readers who enjoy

  • Mathematics readers studying elliptic systems and boundary-value problems
  • Researchers interested in generalized Maxwell equations and Cauchy problems
  • Readers seeking work on fundamental solutions, solvability, and Carleman formulas

Themes

Maxwell-type equationsElliptic systemsCauchy problemsSolvability conditionsCarleman formulas

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Book overview

The monograph is devoted to the study of non-correct problems for a system of Maxwell-type equations with an elliptic complex in a bounded region. We consider the Cauchy problem for an elliptic system of equations of Maxwell type in "n" dimensional space. And also the construction of the matrix of the left fundamental solution of the system of electrodynamics equations of a special kind is given. The generalized Stratton-Chu formula is obtained here, the solvability conditions are proved and the Carleman formula is constructed using the method of bases with double orthogonality, i.e. an explicit formula is constructed which restores the solution of the system of Maxwell's equations in a bounded region.
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