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Eigenoscillations of a fluid in a canonical domain and functional difference equations |
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| Institution: | 1. Department of Physics, Ferdowsi University of Mashhad, 91775-1436 Mashhad, Iran;2. Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran;3. Institute for Metals Superplasticity Problems RAS, Khalturin Street 39, 450001 Ufa, Russia;4. National Research Tomsk State University, Lenin Ave. 36, 634050 Tomsk, Russia;1. College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, PR China;2. Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, PR China;3. Department of Physics, Pondicherry University, Puducherry 605014, India |
| Abstract: | In this work we construct and discuss special solutions of a homogeneous problem for the Laplace equation in a domain with cone-shaped boundaries. The problem at hand is interpreted as that describing oscillatory linear wave movement of a fluid under gravity in such a domain. These solutions are found in terms of the Mellin transform and by means of the reduction to some new functional-difference equations solved in an explicit form (by quadrature). The behavior of the solutions at large distances is studied by use of the saddle point technique. The corresponding eigenoscillations of a fluid are then interpreted as generalized eigenfunctions of the continuous spectrum. |
| Keywords: | Functional equations Eigenoscillations of a fluid Continuous spectrum |
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