The Experts below are selected from a list of 7623 Experts worldwide ranked by ideXlab platform
Norio Kamiya - One of the best experts on this subject based on the ideXlab platform.
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Indirect Trefftz method for boundary value problem of Poisson equation
Engineering Analysis with Boundary Elements, 2003Co-Authors: Eisuke Kita, Y. Ikeda, Norio KamiyaAbstract:Trefftz method is the boundary-type solution procedure using regular T-complete functions satisfying the governing equation. Until now, it has been mainly applied to numerical analyses of the problems governed with the homogeneous differential equations such as the two- and three-dimensional Laplace problems and the two-dimensional elastic problem without body forces. On the other hand, this paper describes the application of the indirect Trefftz method to the solution of the boundary value problems of the two-dimensional Poisson equation. Since the Poisson equation has an Inhomogeneous Term, it is generally difficult to deTermine the T-complete function satisfying the governing equation. In this paper, the Inhomogeneous Term containing an unknown function is approximated by a polynomial in the Cartesian coordinates to deTermine the particular solutions related to the Inhomogeneous Term. Then, the boundary value problem of the Poisson equation is transformed to that of the Laplace equation by using the particular solution. Once the boundary value problem of the Poisson equation is solved according to the ordinary Trefftz formulation, the solution of the boundary value problem of the Poisson equation is estimated from the solution of the Laplace equation and the particular solution. The unknown parameters included in the particular solution are deTermined by the iterative process. The present scheme is applied to some examples in order to examine the numerical properties.
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Solution Of Poisson Equation By Trefftz Method
2002Co-Authors: Eisuke Kita, Y. Ikeda, Norio KamiyaAbstract:This paper describes the application of the Trefftz method to the solution of the boundary value problems of the two-dimensional Poisson equation. The Inhomogeneous Term is approximated by polynomial functions and then, the solution for the Poisson equation is approximated by superposition of the Trefftz functions of the Laplace equation and the particular solutions related to the approximate Inhomogeneous Term. Unknown parameters are deTermined so that the solution satisfies the boundary conditions by means of the collocation method. The present scheme is applied to some examples in order to examine the numerical properties.
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method Solution of Poisson equation by Trefftz
2002Co-Authors: Eisuke Kita, Y Lkeda, Norio KamiyaAbstract:in order to examine the numerical properties. of tjhe collocation method. The present scheme is applied to some examples deTermined so that thc solution satisfies the boundary conditions by means related to t,he approximate Inhomogeneous Term.,Unknown parameters are the Trefftz functions of the Laplace equation and the particular solutions the solution for the Poisson equa.tion is approxima.ted by superposition of Inhomogeneous Term is approximated by polynomial functions and then, the boundary value problems of tjhe two-dimensional Poisson equation. The This paper describes the app1ica.tionof the Trefftz method to the solution of
M. S. Sgibnev - One of the best experts on this subject based on the ideXlab platform.
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Matrix Volterra integral equation with submultiplicative asymptotics of the Inhomogeneous Term
Rendiconti del Circolo Matematico di Palermo Series 2, 2020Co-Authors: M. S. SgibnevAbstract:We consider the matrix Volterra integral equation of the second kind. The Inhomogeneous Term behaves like a submultiplicative function. Asymptotic properties of the solution are established depending on the asymptotics of the submultiplicative function.
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The Discrete Wiener-Hopf Equation with Probability Kernel of Oscillating Type
Siberian Mathematical Journal, 2019Co-Authors: M. S. SgibnevAbstract:We prove the existence of a solution to the discrete Inhomogeneous Wiener-Hopf equation whose kernel is an arithmetic probability distribution generating an oscillating random walk. Asymptotic properties of the solution are established depending on the properties of the Inhomogeneous Term of the equation and its kernel.
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Wiener–Hopf equation whose kernel is a probability distribution
Differential Equations, 2017Co-Authors: M. S. SgibnevAbstract:We prove the existence of a solution of an Inhomogeneous generalized Wiener–Hopf equation whose kernel is a probability distribution on R generating a random walk drifting to +∞, while the Inhomogeneous Term f of the equation belongs to the space L 1(0,∞) or L ∞(0,∞). We establish the asymptotic properties of the solution of this equation under various assumptions about the inhomogeneity f.
Jiakun Liu - One of the best experts on this subject based on the ideXlab platform.
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Boundary regularity for the second boundary-value problem of Monge-Ampère equations in dimension two
arXiv: Analysis of PDEs, 2018Co-Authors: Shibing Chen, Jiakun Liu, Xu-jia WangAbstract:In this paper, we introduce an iteration argument to prove that a convex solution to the Monge-Ampere equation $\mbox{det } D^2 u =f $ in dimension two subject to the natural boundary condition $Du(\Omega) = \Omega^*$ is $C^{2,\alpha}$ smooth up to the boundary. We establish the estimate under the sharp conditions that the Inhomogeneous Term $f\in C^{\alpha}$ and the domains are convex and $C^{1,\alpha}$ smooth. When $f\in C^0$ (resp. $1/C
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Boundary C2,α estimates for Monge–Ampère type equations
Advances in Mathematics, 2015Co-Authors: Yong Huang, Feida Jiang, Jiakun LiuAbstract:Abstract In this paper, we obtain global second derivative estimates for solutions of the Dirichlet problem of certain Monge–Ampere type equations under some structural conditions, while the Inhomogeneous Term is only assumed to be Holder continuous and bounded away from zero and infinity. These estimates correspond to those for the standard Monge–Ampere equation obtained by Trudinger and Wang (2008) [28] and by Savin (2013) [24] , and have natural applications in optimal transportation and prescribed Jacobian equations.
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Interior C 2,alpha regularity for potential functions in optimal transportation
Communications in Partial Differential Equations, 2009Co-Authors: Jiakun Liu, Neil S. Trudinger, Xu-jia WangAbstract:In this paper we study the continuity of second derivatives of solutions to the Monge–Ampere equation arising in optimal transportation. We obtain Holder and more general continuity estimates for second derivatives, when the Inhomogeneous Term is Holder and Dini continuous, together with corresponding regularity results for potentials.
Zuhan Liu - One of the best experts on this subject based on the ideXlab platform.
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Vortex-filaments for Inhomogeneous superconductors in three dimensions
Nonlinear Analysis: Real World Applications, 2010Co-Authors: Zuhan Liu, Ling ZhouAbstract:Abstract In this paper, the asymptotic behavior of solutions to the Ginzburg–Landau system of Inhomogeneous superconductivity in three dimensions was studied with an applied magnetic field | h e x | = O ( | ln e | ) . We show that the limiting singularities set is 1-dimensional rectifiable, which mean curvature was also given. In particular, we study the effect of the Inhomogeneous Term to vortex-filaments.
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ESTIMATES OF LOWER CRITICAL MAGNETIC FIELD AND VORTEX PINNING BY INHOMOGENEITIES IN TYPE II SUPERCONDUCTORS
Chinese Annals of Mathematics, 2004Co-Authors: K. I. Kim, Zuhan LiuAbstract:The effect of an applied magnetic field on an Inhomogeneous superconductor is studied and the value of the lower critical magnetic field Hc1 at which superconducting vortices appear is estimated. In addition, the authors locate the vortices of local minimizers, which depends on the Inhomogeneous Term a(x).
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ESTIMATE OF THE UPPER CRITICAL FIELD AND CONCENTRATION FOR SUPERCONDUCTOR
Chinese Annals of Mathematics, 2004Co-Authors: K. I. Kim, Zuhan LiuAbstract:The effect of an applied magnetic field on an Inhomogeneous superconductor is studied and the value of the upper critical magnetic field Hc3 at which superconductivity can nucleate is estimated. In addition, the authors locate the concentration of the order parameter, which depends on the Inhomogeneous Term a(x). Unlikely to the homogeneous case, the order parameter may concentrate in the interior of the superconducting material, due to the influence of the Inhomogeneous Term a(x).
Eisuke Kita - One of the best experts on this subject based on the ideXlab platform.
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Indirect Trefftz method for boundary value problem of Poisson equation
Engineering Analysis with Boundary Elements, 2003Co-Authors: Eisuke Kita, Y. Ikeda, Norio KamiyaAbstract:Trefftz method is the boundary-type solution procedure using regular T-complete functions satisfying the governing equation. Until now, it has been mainly applied to numerical analyses of the problems governed with the homogeneous differential equations such as the two- and three-dimensional Laplace problems and the two-dimensional elastic problem without body forces. On the other hand, this paper describes the application of the indirect Trefftz method to the solution of the boundary value problems of the two-dimensional Poisson equation. Since the Poisson equation has an Inhomogeneous Term, it is generally difficult to deTermine the T-complete function satisfying the governing equation. In this paper, the Inhomogeneous Term containing an unknown function is approximated by a polynomial in the Cartesian coordinates to deTermine the particular solutions related to the Inhomogeneous Term. Then, the boundary value problem of the Poisson equation is transformed to that of the Laplace equation by using the particular solution. Once the boundary value problem of the Poisson equation is solved according to the ordinary Trefftz formulation, the solution of the boundary value problem of the Poisson equation is estimated from the solution of the Laplace equation and the particular solution. The unknown parameters included in the particular solution are deTermined by the iterative process. The present scheme is applied to some examples in order to examine the numerical properties.
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Solution Of Poisson Equation By Trefftz Method
2002Co-Authors: Eisuke Kita, Y. Ikeda, Norio KamiyaAbstract:This paper describes the application of the Trefftz method to the solution of the boundary value problems of the two-dimensional Poisson equation. The Inhomogeneous Term is approximated by polynomial functions and then, the solution for the Poisson equation is approximated by superposition of the Trefftz functions of the Laplace equation and the particular solutions related to the approximate Inhomogeneous Term. Unknown parameters are deTermined so that the solution satisfies the boundary conditions by means of the collocation method. The present scheme is applied to some examples in order to examine the numerical properties.
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method Solution of Poisson equation by Trefftz
2002Co-Authors: Eisuke Kita, Y Lkeda, Norio KamiyaAbstract:in order to examine the numerical properties. of tjhe collocation method. The present scheme is applied to some examples deTermined so that thc solution satisfies the boundary conditions by means related to t,he approximate Inhomogeneous Term.,Unknown parameters are the Trefftz functions of the Laplace equation and the particular solutions the solution for the Poisson equa.tion is approxima.ted by superposition of Inhomogeneous Term is approximated by polynomial functions and then, the boundary value problems of tjhe two-dimensional Poisson equation. The This paper describes the app1ica.tionof the Trefftz method to the solution of
