Riemann integral operator for stationary and non-stationary processes. (English. Russian original) Zbl 1485.35151
Cybern. Syst. Anal. 57, No. 6, 918-926 (2021); translation from Kibern. Sist. Anal. 57, No. 6, 84-93 (2021).
Summary: Integral operators based on the Riemann function, which transform arbitrary analytical functions into regular solutions of equations of elliptic, parabolic, and hyperbolic types of second order, are constructed. The Riemann operator method is generalized for the biaxisymmetric Helmholtz equation. A method for finding solutions to the above equations in analytical form is developed. In some cases, formulas for inverting integral representations of solutions are constructed. The conditions for solving the Cauchy problem for the axisymmetric Helmholtz equation are formulated.
MSC:
| 35J15 | Second-order elliptic equations |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 35K10 | Second-order parabolic equations |
| 35L10 | Second-order hyperbolic equations |
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