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This article is cited in 8 scientific papers (total in 8 papers)
Two physical applications of the Laplace operator perturbed on a null set
I. Yu. Popov, D. A. Zubok St. Petersburg State University of Information Technologies, Mechanics and Optics
Abstract:
Two physical applications of the Laplace operator perturbed on a set of zero measure are suggested. The approach is based on the theory of self-adjoint extensions of symmetrical operators. The first application is a solvable model of scattering of a plane wave by a perturbed thin cylinder. “Nonlocal” extensions are described. The model parameters can be chosen such that the model solution is an approximation of the corresponding “realistic” solution. The second application is the description of the time evolution of a one-dimensional quasi-Chaplygin medium, which can be reduced using a hodograph transform to the ill-posed problem of the Laplace operator perturbed on a set of codimension two in $\mathbf R^3$. Stability and instability conditions are obtained.
Received: 02.09.1998 Revised: 02.11.1998
Citation:
I. Yu. Popov, D. A. Zubok, “Two physical applications of the Laplace operator perturbed on a null set”, TMF, 119:2 (1999), 295–307; Theoret. and Math. Phys., 119:2 (1999), 629–639
Linking options:
https://www.mathnet.ru/eng/tmf740https://doi.org/10.4213/tmf740 https://www.mathnet.ru/eng/tmf/v119/i2/p295
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Abstract page: | 460 | Full-text PDF : | 179 | References: | 50 | First page: | 1 |
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