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Remigio Russo - One of the best experts on this subject based on the ideXlab platform.
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the existence of a solution with finite dirichlet integral for the steady navier stokes equations in a plane exterior symmetric Domain
Journal de Mathématiques Pures et Appliquées, 2014Co-Authors: Mikhail V Korobkov, Konstantin Pileckas, Remigio RussoAbstract:Abstract We study the nonhomogeneous boundary value problem for the Navier–Stokes equations of steady motion of a viscous incompressible fluid in a two-dimensional exterior Multiply Connected Domain R 2 ∖ ( ⋃ j = 1 N Ω ¯ j ) . We prove that this problem has a solution if Ω and the boundary datum are axially symmetric. We have no restriction on fluxes, in particular, they could be arbitrary large.
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on the flux problem in the theory of steady navier stokes equations with nonhomogeneous boundary conditions
Archive for Rational Mechanics and Analysis, 2013Co-Authors: Mikhail V Korobkov, Konstantin Pileckas, Remigio RussoAbstract:We study the nonhomogeneous boundary value problem for Navier–Stokes equations of steady motion of a viscous incompressible fluid in a two-dimensional, bounded, Multiply Connected Domain \({\Omega = \Omega_1 \backslash \overline{\Omega}_2, \overline\Omega_2\subset \Omega_1}\) . We prove that this problem has a solution if the flux \({\mathcal{F}}\) of the boundary value through ∂Ω2 is nonnegative (inflow condition). The proof of the main result uses the Bernoulli law for a weak solution to the Euler equations and the one-sided maximum principle for the total head pressure corresponding to this solution.
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the existence theorem for steady navier stokes equations in the axially symmetric case
arXiv: Mathematical Physics, 2011Co-Authors: Mikhail V Korobkov, Konstantin Pileckas, Remigio RussoAbstract:We study the nonhomogeneous boundary value problem for Navier-Stokes equations of steady motion of a viscous incompressible fluid in a three-dimensional bounded Multiply Connected Domain. We prove that this problem has a solution in some axially symmetric cases, in particular, when all components of the boundary intersect the axis of symmetry.
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on the flux problem in the theory of steady navier stokes equations with nonhomogeneous boundary conditions
arXiv: Mathematical Physics, 2010Co-Authors: Mikhail V Korobkov, Konstantin Pileckas, Remigio RussoAbstract:We study the nonhomogeneous boundary value problem for Navier--Stokes equations of steady motion of a viscous incompressible fluid in a two--dimensional bounded Multiply Connected Domain $\Omega=\Omega_1\setminus\bar{\Omega}_2, \;\bar\Omega_2\subset \Omega_1$. We prove that this problem has a solution if the flux $\F$ of the boundary value through $\partial\Omega_2$ is nonnegative. The proof of the main result uses the Bernoulli law for a weak solution to the Euler equations and the one-side maximum principle for the total head pressure corresponding to this solution.
P. A. Krutitskii - One of the best experts on this subject based on the ideXlab platform.
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the impedance problem for the propagative helmholtz equation in interior Multiply Connected Domain
Computers & Mathematics With Applications, 2003Co-Authors: P. A. KrutitskiiAbstract:Abstract The impedance problem for the propagative Helmholtz equation in the interior Multiply Connected Domain is studied in two and three dimensions by a special modification of a boundary integral equation method. Additional boundaries are introduced inside interior parts of the boundary of the Domain. The solution of the problem is obtained in the form of a single layer potential on the whole boundary. The density in the potential satisfies the uniquely solvable Fredholm equation of the second kind and can be computed by standard codes. In fact, our method holds for any positive wave numbers.
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initial boundary value problem for an equation of internal gravity waves in a 3 d Multiply Connected Domain with dirichlet boundary condition
Advances in Mathematics, 2003Co-Authors: P. A. KrutitskiiAbstract:Abstract Method of boundary integral equations is applied to the initial–boundary value problem for an equation of fourth order and composite type in 3-D Multiply Connected Domain with Dirichlet boundary condition. The problem controls nonsteady internal gravity waves in a stratified fluid. The problem is reduced to the time-dependent integral equation. It is shown that the integral equation is solvable. The solution of the problem is obtained in the form of dynamic potentials. The density in potentials obeys this integral equation. Therefore, the existence theorem is proved. Besides, the uniqueness of the solution is studied. All results hold for both interior and exterior Domains with appropriate conditions at infinity.
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the dirichlet problem for the two dimensional laplace equation in a Multiply Connected Domain with cuts
Proceedings of the Edinburgh Mathematical Society, 2000Co-Authors: P. A. KrutitskiiAbstract:The Dirichlet problem for the Laplace equation in a Connected-plane region with cuts is studied. The existence of a classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable.
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the dirichlet problem for the 2 d helmholtz equation in a Multiply Connected Domain with cuts
Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 1997Co-Authors: P. A. KrutitskiiAbstract:The Dirichler problem for the dissipative Helmholts equation in a Connected plane region with cuts is studied. The existence of a classical solution is proved by potential theory. The problme is reduced to a Fredholm equation of second kind, which is uniquely solvable.
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the first initial boundary value problem for the gravity inertia wave equation in a Multiply Connected Domain
Computational Mathematics and Mathematical Physics, 1997Co-Authors: P. A. KrutitskiiAbstract:An existence and uniqueness theorem is proved for the solution to the first initial-boundary value problem for the gravity-inertia wave equation in a Multiply Connected Domain. The problem is reduced to uniquely solvable integral equations on the Domain boundary by applying the dynamic-potential theory developed for the gravity-inertia wave equation.
Mikhail V Korobkov - One of the best experts on this subject based on the ideXlab platform.
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the existence of a solution with finite dirichlet integral for the steady navier stokes equations in a plane exterior symmetric Domain
Journal de Mathématiques Pures et Appliquées, 2014Co-Authors: Mikhail V Korobkov, Konstantin Pileckas, Remigio RussoAbstract:Abstract We study the nonhomogeneous boundary value problem for the Navier–Stokes equations of steady motion of a viscous incompressible fluid in a two-dimensional exterior Multiply Connected Domain R 2 ∖ ( ⋃ j = 1 N Ω ¯ j ) . We prove that this problem has a solution if Ω and the boundary datum are axially symmetric. We have no restriction on fluxes, in particular, they could be arbitrary large.
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on the flux problem in the theory of steady navier stokes equations with nonhomogeneous boundary conditions
Archive for Rational Mechanics and Analysis, 2013Co-Authors: Mikhail V Korobkov, Konstantin Pileckas, Remigio RussoAbstract:We study the nonhomogeneous boundary value problem for Navier–Stokes equations of steady motion of a viscous incompressible fluid in a two-dimensional, bounded, Multiply Connected Domain \({\Omega = \Omega_1 \backslash \overline{\Omega}_2, \overline\Omega_2\subset \Omega_1}\) . We prove that this problem has a solution if the flux \({\mathcal{F}}\) of the boundary value through ∂Ω2 is nonnegative (inflow condition). The proof of the main result uses the Bernoulli law for a weak solution to the Euler equations and the one-sided maximum principle for the total head pressure corresponding to this solution.
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the existence theorem for steady navier stokes equations in the axially symmetric case
arXiv: Mathematical Physics, 2011Co-Authors: Mikhail V Korobkov, Konstantin Pileckas, Remigio RussoAbstract:We study the nonhomogeneous boundary value problem for Navier-Stokes equations of steady motion of a viscous incompressible fluid in a three-dimensional bounded Multiply Connected Domain. We prove that this problem has a solution in some axially symmetric cases, in particular, when all components of the boundary intersect the axis of symmetry.
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on the flux problem in the theory of steady navier stokes equations with nonhomogeneous boundary conditions
arXiv: Mathematical Physics, 2010Co-Authors: Mikhail V Korobkov, Konstantin Pileckas, Remigio RussoAbstract:We study the nonhomogeneous boundary value problem for Navier--Stokes equations of steady motion of a viscous incompressible fluid in a two--dimensional bounded Multiply Connected Domain $\Omega=\Omega_1\setminus\bar{\Omega}_2, \;\bar\Omega_2\subset \Omega_1$. We prove that this problem has a solution if the flux $\F$ of the boundary value through $\partial\Omega_2$ is nonnegative. The proof of the main result uses the Bernoulli law for a weak solution to the Euler equations and the one-side maximum principle for the total head pressure corresponding to this solution.
Jengtzong Chen - One of the best experts on this subject based on the ideXlab platform.
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eigensolutions of the helmholtz equation for a Multiply Connected Domain with circular boundaries using the multipole trefftz method
Engineering Analysis With Boundary Elements, 2010Co-Authors: Jengtzong ChenAbstract:In this paper, 2D eigenproblems with the Multiply Connected Domain are studied by using the multipole Trefftz method. We extend the conventional Trefftz method to the multipole Trefftz method by introducing the multipole expansion. The addition theorem is employed to expand the Trefftz bases to the same polar coordinates centered at one circle, where boundary conditions are specified. Owing to the introduction of the addition theorem, collocation techniques are not required to construct the linear algebraic system. Eigenvalues and eigenvectors can be found at the same time by employing the singular value decomposition (SVD). To deal with the eigenproblems, the present method is free of pollution of spurious eigenvalues. Both the eigenvalues and eigenmodes compare well with those obtained by analytical methods and the BEM as shown in illustrative examples.
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regularized meshless method for solving acoustic eigenproblem with Multiply Connected Domain
Cmes-computer Modeling in Engineering & Sciences, 2006Co-Authors: K.h. Chen, Jengtzong ChenAbstract:In this paper, we employ the regularized meshless method (RMM) to search for eigenfrequency of two-dimension acoustics with Multiply-Connected do- main. The solution is represented by using the double layer potentials. The source points can be located on the physical boundary not alike method of fundamental so- lutions (MFS) after using the proposed technique to reg- ularize the singularity and hypersingularity of the ker- nel functions. The troublesome singularity in the MFS methods is desingularized and the diagonal terms of in- fluence matrices are determined by employing the sub- tracting and adding-back technique. Spurious eigenval- ues are filtered out by using singular value decomposi- tion (SVD) updating term technique. The accuracy and stability of the RMM are verified through the numerical experiments of the Dirichlet and Neumann problems for Domainswithmultipleholes. Themethod isfoundtoper- form pretty well in comparison with analytical solutions and numerical resultsof boundaryelement method, finite element method and the point-matching method. keyword: Regularized meshless method, Hypersingu- larity, Eigenvalue, Eigenmode, Method of fundamental solutions,Acoustics.
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regularized meshless method for Multiply Connected Domain laplace problems
Engineering Analysis With Boundary Elements, 2006Co-Authors: K.h. Chen, Jengtzong Chen, D.l. Young, M-c LuAbstract:Abstract In this paper, the regularized meshless method (RMM) is developed to solve two-dimensional Laplace problem with Multiply-Connected Domain. The solution is represented by using the double-layer potential. The source points can be located on the physical boundary by using the proposed technique to regularize the singularity and hypersingularity of the kernel functions. The troublesome singularity in the traditional methods is avoided and the diagonal terms of influence matrices are easily determined. The accuracy and stability of the RMM are verified in numerical experiments of the Dirichlet, Neumann, and mixed-type problems under a Domain having multiple holes. The method is found to perform pretty well in comparison with the boundary element method.
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boundary element analysis for the helmholtz eigenvalue problems with a Multiply Connected Domain
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2001Co-Authors: Jengtzong Chen, S W ChyuanAbstract:For a Helmholtz eigenvalue problem with a Multiply Connected Domain, the boundary integral equation approach as well as the boundary-element method is shown to yield spurious eigenvalues even if the complex-valued kernel is used. In such a case, it is found that spurious eigenvalues depend on the geometry of the inner boundary. Demonstrated as an analytical case, the spurious eigenvalue for a Multiply Connected problem with its inner boundary as a circle is studied analytically. By using the degenerate kernels and circulants, an annular case can be studied analytically in a discrete system and can be treated as a special case. The proof for the general boundary instead of the circular boundary is also derived. The Burton-Miller method is employed to eliminate spurious eigenvalues in the Multiply Connected case. Moreover, a modified method considering only the real-part formulation is provided. Five examples are shown to demonstrate that the spurious eigenvalues depend on the shape of the inner boundary. Good agreement between analytical prediction and numerical results are found.
Konstantin Pileckas - One of the best experts on this subject based on the ideXlab platform.
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the existence of a solution with finite dirichlet integral for the steady navier stokes equations in a plane exterior symmetric Domain
Journal de Mathématiques Pures et Appliquées, 2014Co-Authors: Mikhail V Korobkov, Konstantin Pileckas, Remigio RussoAbstract:Abstract We study the nonhomogeneous boundary value problem for the Navier–Stokes equations of steady motion of a viscous incompressible fluid in a two-dimensional exterior Multiply Connected Domain R 2 ∖ ( ⋃ j = 1 N Ω ¯ j ) . We prove that this problem has a solution if Ω and the boundary datum are axially symmetric. We have no restriction on fluxes, in particular, they could be arbitrary large.
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on the flux problem in the theory of steady navier stokes equations with nonhomogeneous boundary conditions
Archive for Rational Mechanics and Analysis, 2013Co-Authors: Mikhail V Korobkov, Konstantin Pileckas, Remigio RussoAbstract:We study the nonhomogeneous boundary value problem for Navier–Stokes equations of steady motion of a viscous incompressible fluid in a two-dimensional, bounded, Multiply Connected Domain \({\Omega = \Omega_1 \backslash \overline{\Omega}_2, \overline\Omega_2\subset \Omega_1}\) . We prove that this problem has a solution if the flux \({\mathcal{F}}\) of the boundary value through ∂Ω2 is nonnegative (inflow condition). The proof of the main result uses the Bernoulli law for a weak solution to the Euler equations and the one-sided maximum principle for the total head pressure corresponding to this solution.
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the existence theorem for steady navier stokes equations in the axially symmetric case
arXiv: Mathematical Physics, 2011Co-Authors: Mikhail V Korobkov, Konstantin Pileckas, Remigio RussoAbstract:We study the nonhomogeneous boundary value problem for Navier-Stokes equations of steady motion of a viscous incompressible fluid in a three-dimensional bounded Multiply Connected Domain. We prove that this problem has a solution in some axially symmetric cases, in particular, when all components of the boundary intersect the axis of symmetry.
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on the flux problem in the theory of steady navier stokes equations with nonhomogeneous boundary conditions
arXiv: Mathematical Physics, 2010Co-Authors: Mikhail V Korobkov, Konstantin Pileckas, Remigio RussoAbstract:We study the nonhomogeneous boundary value problem for Navier--Stokes equations of steady motion of a viscous incompressible fluid in a two--dimensional bounded Multiply Connected Domain $\Omega=\Omega_1\setminus\bar{\Omega}_2, \;\bar\Omega_2\subset \Omega_1$. We prove that this problem has a solution if the flux $\F$ of the boundary value through $\partial\Omega_2$ is nonnegative. The proof of the main result uses the Bernoulli law for a weak solution to the Euler equations and the one-side maximum principle for the total head pressure corresponding to this solution.
