Solving of initial-boundary value problems for the wave equation using retarded surface potential and Laguerre transform (in Ukrainian)

Author
S. V. Litynskyy, A. O. Muzychuk
Ivan Franko National University of Lviv
Abstract
Approach for solving of initial-boundary value problems for the homogeneous wave equation is described and proved. It is based on the Laguerre transform in the time domain and the boundary integral equations. Retarded potentials are used for representation of generalized solutions of such problems. The densities of retarded potentials are expanded in Fourier-Laguerre series which coefficients have special convolution form. As a result, initial-boundary value problems are reduced to a sequence of boundary integral equations.
Keywords
initial-boundary value problem; wave equation; Sobolev spaces; generalized solution; retarded surface potentials; Laguerre transform; time domain boundary integral equations
DOI
doi:10.15330/ms.44.2.185-203
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Pages
185-203
Volume
44
Issue
2
Year
2015
Journal
Matematychni Studii
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