Interaction between thermoelastic and scalar oscillation fields

“…In [30,31] the interface problems of the interaction between a four-dimensional thermoelastic field and a scalar oscillation field have been studied in general homogeneous anisotropic case.…”

Section: Communicated By E Meistermentioning

confidence: 99%

“…The analysis of these PsDEs (uniqueness, index problem and existence), besides the radiation conditions for the scalar acoustic field, in addition, needs special, the so-called generalized Sommerfeld-Kupradze type radiation conditions for elastic (thermoelastic) field (for details see [46,49,30,31]). These latter conditions are too complicated in anisotropic case.…”

Section: Communicated By E Meistermentioning

confidence: 99%

“…Now we are in the position to define the class Som P ( \) of complex-valued functions satisfying the generalized Sommerfeld type radiation conditions (see [61,30,31]). …”

Section: Scalar Fieldmentioning

confidence: 99%

“…(x) represents the fundamental function for the operator a(D) (see (1.8)). Now we list here some results obtained in [31]. …”

Section: Integral Representation Formulae and Potentialsmentioning

confidence: 99%

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Non-local approach in mathematical problems of fluid-structure interaction

Jentsch

Natroshvili

1999

Math. Meth. Appl. Sci.

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Three‐dimensional mathematical problems of interaction between elastic and scalar oscillation fields are investigated. An elastic field is to be defined in a bounded inhomogeneous anisotropic body occupying the domain Ω¯1⊂ℝ3 while a physical (acoustic) scalar field is to be defined in the exterior domain Ω¯2=ℝ3\Ω1 which is filled up also by an anisotropic (fluid) medium. These two fields satisfy the governing equations of steady‐state oscillations in the corresponding domains together with special kinematic and dynamic transmission conditions on the interface ∂Ω1. The problems are studied by the so‐called non‐local approach, which is the coupling of the boundary integral equation method (in the unbounded domain) and the functional‐variational method (in the bounded domain). The uniqueness and existence theorems are proved and the regularity of solutions are established with the help of the corresponding Steklov–Poincaré type operators and on the basis of the Gårding inequality and the Lax–Milgram theorem. In particular, it is shown that the physical fluid–solid acoustic interaction problem is solvable for arbitrary values of the frequency parameter. Copyright © 1999 John Wiley & Sons, Ltd.

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Boundary integral method for thermoelastic screen scattering problem in ?3

Cakoni

2000

Math. Meth. Appl. Sci.

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We investigate a three‐dimensional mathematical thermoelastic scattering problem from an open surface which will be referred to as a screen. Under the assumption of the local finite energy of the unified thermoelastic scattered field, we give a weak model on the appropriate Sobolev spaces and derive equivalent integral equations of the first kind for the jump of some trace operators on the open surface. Uniqueness and existence theorems are proved, the regularity and the singular behaviour of the solution near the edge are established with the help of the Wiener–Hopf method in the halfspace, the calculus of pseudodifferential operators on the basis of the strong ellipticity property and Gårding's inequality. An improved Galerkin scheme is provided by simulating the singular behaviour of the exact solution at the edge of the screen. Copyright © 2000 John Wiley & Sons, Ltd.

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Interaction between thermoelastic and scalar oscillation fields

Cited by 10 publications

References 22 publications

Cylindrical vibration of an elastic cusped plate under the action of an incompressible fluid in case ofN = 0 approximation of I. Vekuas hierarchical models

Cylindrical vibration of an elastic cusped plate under the action of an incompressible fluid in case ofN = 0 approximation of I. Vekuas hierarchical models

Non-local approach in mathematical problems of fluid-structure interaction

Boundary integral method for thermoelastic screen scattering problem in ?3

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