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This article is cited in 3 scientific papers (total in 3 papers)
Mathematics
On the connection between solutions of initial boundary-value problems for a some class of integro-differential PDE and a linear hyperbolic equation
P. N. Burago, A. I. Egamov National Research Lobachevsky State University of Nizhny Novgorod
Abstract:
We consider the second initial boundary-value problem for a certain class of second-order integro-differential PDE with integral operator. The connection of its solution with the solution of the standard second linear initial boundary-value problem for the hyperbolic equation is shown. Thus, the nonlinear problem is reduced to a standard linear problem, whose numerical solution can be obtained, for example, by the Fourier method or Galerkin method.
The article provides examples of five integro-differential equations for various integral operators as particular representatives of the class of integro-differential equations for a better understanding of the problem. The application of the main theorem to these examples is shown. Some simple natural requirement is imposed on the integral operator; so, in four cases out of five the problem's solution satisfies some phase constraint. The form of these constraints is of particular interest for the further research.
Keywords:
the second initial boundary value problem, integro-differential equation with PDE, phase constraint, hyperbolic equation.
Citation:
P. N. Burago, A. I. Egamov, “On the connection between solutions of initial boundary-value problems for a some class of integro-differential PDE and a linear hyperbolic equation”, Zhurnal SVMO, 21:4 (2019), 413–429
Linking options:
https://www.mathnet.ru/eng/svmo750 https://www.mathnet.ru/eng/svmo/v21/i4/p413
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Abstract page: | 298 | Full-text PDF : | 64 | References: | 43 |
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