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Захаров, Е. В.; Safronov, S. I.; Tarasov, R. P.

doi:10.1023/a:1021784103185

Cited by 4 publications

(7 citation statements)

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“…Noncommutative harmonic analysis on a surface S with a discontinuous action of the dihedral group D n permits one to represent solutions of the boundary equations of boundary value problems with rotational symmetry in the form of Fourier series of functions on D n ranging in a function space on the fundamental domain of D n . This representation was used in [4] in the construction of an analytic-numerical solution of the problem of acoustically soft scattering by a closed surface of revolution partly screened by a surface of revolution with a hole. The problem of acoustically soft scattering of a plane wave by a cone enclosed in a sphere with a hole was considered in [4] by way of a particular computational application.…”

Section: The Grid Boundary Equations Of the Problem Of Soft Acoustic mentioning

confidence: 99%

“…This representation was used in [4] in the construction of an analytic-numerical solution of the problem of acoustically soft scattering by a closed surface of revolution partly screened by a surface of revolution with a hole. The problem of acoustically soft scattering of a plane wave by a cone enclosed in a sphere with a hole was considered in [4] by way of a particular computational application.…”

Section: The Grid Boundary Equations Of the Problem Of Soft Acoustic mentioning

confidence: 99%

“…In what follows, we use the results in [1][2][3][4] to construct computational schemes for solving Eq. (6) on a thick shell and a screen with a rotational symmetry.…”

Section: The Grid Boundary Equations Of the Problem Of Soft Acoustic mentioning

confidence: 99%

“…The results of [1] were used in the construction of numerical schemes for scalar problems such as problems of acoustic excitation of an axisymmetric domain with two-component boundary through a hole on the boundary [2] and the problem of resonance scattering by a hole on an acoustically soft surface of revolution [3].…”

Section: Introductionmentioning

confidence: 99%

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Resonance excitation of the interior of an acoustically soft thick shell through a screened hole

2004

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Section: The Grid Boundary Equations Of the Problem Of Soft Acoustic mentioning

confidence: 99%

Section: The Grid Boundary Equations Of the Problem Of Soft Acoustic mentioning

confidence: 99%

“…In what follows, we use the results in [1][2][3][4] to construct computational schemes for solving Eq. (6) on a thick shell and a screen with a rotational symmetry.…”

Section: The Grid Boundary Equations Of the Problem Of Soft Acoustic mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Resonance excitation of the interior of an acoustically soft thick shell through a screened hole

2004

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“…For a resonator with infinitely thin walls, the singularly perturbed Dirichlet boundary value problem for the Helmholtz equation admits numerical analysis on the basis of a boundary integral equation of the first kind. (See [7,8] for the case of resonance excitation and [7,9] for the case of resonance scattering by a hole.) In what follows, in the framework of the formalism developed in [7,9], we perform a numerical analysis of scattering by a cross-shaped hole on an acoustically smooth boundary surface near a resonance of the interior domain; moreover, we give a more detailed description than in [9] of the structure relations underlying the numerical analysis of the singularly perturbed Dirichlet problem for the Helmholtz equation corresponding to a resonator with infinitely thin walls.…”

Section: Introductory Remarksmentioning

confidence: 99%

Acoustic Scattering by a Cross-Shaped Hole on a Smooth Boundary Surface Near a Resonance Point of the Interior Domain

2005

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INTRODUCTORY REMARKSThe Dirichlet problem corresponding to a resonator with walls of finite thickness is a wellknown singularly perturbed boundary value problem for the Helmholtz equation and has been studied quite comprehensively. The resonator has the form Ω ε = Ω i ∪ Ω e ∪ κ ε , where Ω i and Ω e are the disjoint components of the complement of a domain diffeomorphic to a spherical layer and κ ε is a small hole that joins these components and has the size of the order of ε 1. It was shown in [1] that the analytic continuation of the solution of this problem into the lower complex half-plane of the spectral parameter has poles with small imaginary part close to the eigenvalues of the Dirichlet Laplacian −∆ Ωi . The poles of a resonator with finite walls were analyzed in [2-6] by various methods as ε → 0. There is a closely related problem of resonance excitation of a domain through a hole on an acoustically smooth boundary surface and the problem of scattering by a hole on an acoustically smooth boundary surface near the resonance of the interior domain, both problems corresponding to a resonator with infinitely thin walls. For a resonator with infinitely thin walls, the singularly perturbed Dirichlet boundary value problem for the Helmholtz equation admits numerical analysis on the basis of a boundary integral equation of the first kind. (See [7,8] for the case of resonance excitation and [7,9] for the case of resonance scattering by a hole.) In what follows, in the framework of the formalism developed in [7,9], we perform a numerical analysis of scattering by a cross-shaped hole on an acoustically smooth boundary surface near a resonance of the interior domain; moreover, we give a more detailed description than in [9] of the structure relations underlying the numerical analysis of the singularly perturbed Dirichlet problem for the Helmholtz equation corresponding to a resonator with infinitely thin walls.

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Generalized solvability and optimization of a parabolic system with a discontinuous solution

Nomirovskii

2007

Journal of Differential Equations

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We consider the following linear parabolic system in a domain with a thin low-permeable insertion ("imperfect interface"):We consider a new formulation of the problem where the unknowns are (u, ω), and the parabolic problem is converted to a first-order system of partial differential equations with distributional coefficients. We also prove inequalities for negative norms for the parabolic operator with the distributional coefficients and theorems of existence and uniqueness. For optimization problems for the processes we show existence of optimal controls, investigate smoothness of a performance criterion and give a simple condition for controllability of the system. In addition, we consider applications of the obtained results to a pulse control problem and prove convergence of a control mapping regularization procedure.

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Cited by 4 publications

References 1 publication

Resonance excitation of the interior of an acoustically soft thick shell through a screened hole

Resonance excitation of the interior of an acoustically soft thick shell through a screened hole

Acoustic Scattering by a Cross-Shaped Hole on a Smooth Boundary Surface Near a Resonance Point of the Interior Domain

Generalized solvability and optimization of a parabolic system with a discontinuous solution

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