ON INITIAL BOUNDARY VALUE PROBLEMS FOR THE DEGENERATE 1D WAVE EQUATION

Vladimir V. Borsch

Анотація


Initial boundary value problems in space-time rectangle for the following linear inhomogeneous degenerate wave equation of the second order smooth coefficient function a(x) vanishes in single points of segment.
The well-posedness of the initial boundary value problems is achieved using some approaches to regularization of the equation and the theory of characteristics. The problems for wave equation are then reduced to problems for hyperbolic balance laws 2 and 3 of partial differential equations of the first order. Weak solutions to the problems are obtained using proper numerical methods.
Results obtained for some approaches to regularization are presented.


Ключові слова


degenerate wave equations; the theory of characteristics

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DOI: http://dx.doi.org/10.15421/141906

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