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A representation of the solution of the Cauchy problem for a degenerate hyperbolic equation in several independent variables. (English) Zbl 0755.35074

Topics in mathematical analysis, Vol. Dedicated Mem. of A. L. Cauchy, Ser. Pure Math. 11, 456-477 (1989).
Summary: [For the entire collection see Zbl 0721.00014.]
We deal with a degenerate hyperbolic equation which is invariant under a transformation group. First, using a geometric method, we obtain the fundamental solution of this equation. Then by the Green integral formula we give the solution of its Cauchy problem explicitly.

MSC:

35L80 Degenerate hyperbolic equations
35C15 Integral representations of solutions to PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
35A08 Fundamental solutions to PDEs
35L15 Initial value problems for second-order hyperbolic equations
58J70 Invariance and symmetry properties for PDEs on manifolds

Biographic References:

Cauchy, A. L.

Citations:

Zbl 0721.00014
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