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An explicit solution of the pseudo‐hyperbolic initial boundary value problem in a multiply connected region
Author(s) -
Krutitskii Pavel A.
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670181105
Subject(s) - mathematics , boundary value problem , uniqueness , mathematical analysis , initial value problem , boundary (topology) , mixed boundary condition , free boundary problem , hyperbolic partial differential equation , robin boundary condition , partial differential equation
An explicit solution of the pseudo‐hyperbolic initial boundary value problem with a mixed boundary condition has been constructed. The problem describes the propagation of non‐stationary internal waves in a stratified and rotational fluid. The generation of waves is caused by small oscillations of double‐sided plates beginning at time t = 0. Dynamic pressure is specified on one set of plates and this yields the first boundary condition. Normal velocities are specified on another set of plates and this leads to an analogue of the second boundary condition with time derivatives. The solution has been obtained by the method of non‐classical time‐dependent dynamic potentials. The uniqueness of the solution has been studied.