Nonstationary boundary value problems for wave equation and their generalized solutions

Details Nonstationary boundary value problems for wave equation and their generalized solutions Nonstationary boundary value problems for wave equation and their generalized solutions

2006-10-18

arxiv.org/abs/math/0610544v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

The multivariate analogue of Dalamber's equation in the space of generalized functions is considered. The method of generalized functions for the building of solutions of nonstationary boundary value problems for wave equations in spaces of different dimensions is elaborated. Dynamic analogues of Green and Gauss formulas for solutions of wave equation in the space of generalized functions are built. Their regular integral representations and singular boundary integral equations for solving the nonstationary problems are constructed for the spaces of the dimensions 1,2,3. The method of obtaining of conditions on fronts of shock waves is stated.

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