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 Applied Mathematics & Physics: Year: Volume: Issue: Page: Find

 Applied Mathematics & Physics, 2019, Volume 51, Issue 4, Pages 506–513 (Mi pmf29)

MATHEMATICS

Generalized divergent theorem and second Green identity of $B-$elliptic and $B-$hyperbolic operators

E. L. Shishkina

University of Information Technology and Management

Abstract: The article presents a generalization of the divergence theorem, which establishes a connection between the weight divergence of a vector field and the derivative in the direction from the same vector field corrected by power weights. From this generalization, two formulas of the type of the second Green identity follow for the cases when the Bessel operator acts instead of the each second derivative in the operators of elliptic and hyperbolic types. The classical second Green identity is of great importance in mathematical physics, because, for example, with its help the uniqueness of the solution of the Cauchy problem for the wave equation is established. The generalization of this identity obtained in the article can be used to prove the uniqueness of the solution of the Cauchy problem for the general Euler-Poisson-Darboux equation.

DOI: https://doi.org/10.18413/2075-4639-2019-51-4-506-513

UDC: 517.9