• Title, Summary, Keyword: Neumann problem

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UNIQUENESS OF IDENTIFYING THE CONVECTION TERM

  • Cheng, Jin;Gen Nakamura;Erkki Somersalo
    • Communications of the Korean Mathematical Society
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    • v.16 no.3
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    • pp.405-413
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    • 2001
  • The inverse boundary value problem for the steady state heat equation with convection term is considered in a simply connected bounded domain with smooth boundary. Taking the Dirichlet to Neumann map which maps the temperature on the boundary to the that flux on the boundary as an observation data, the global uniqueness for identifying the convection term from the Dirichlet to Neumann map is proved.

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EXISTENCE OF A POSITIVE INFIMUM EIGENVALUE FOR THE p(x)-LAPLACIAN NEUMANN PROBLEMS WITH WEIGHTED FUNCTIONS

  • Kim, Yun-Ho
    • Korean Journal of Mathematics
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    • v.22 no.3
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    • pp.395-406
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    • 2014
  • We study the following nonlinear problem $-div(w(x){\mid}{\nabla}u{\mid}^{p(x)-2}{\nabla}u)+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u)$ in ${\Omega}$ which is subject to Neumann boundary condition. Under suitable conditions on w and f, we give the existence of a positive infimum eigenvalue for the p(x)-Laplacian Neumann problem.

NOTE ON LOCAL BOUNDEDNESS FOR WEAK SOLUTIONS OF NEUMANN PROBLEM FOR SECOND-ORDER ELLIPTIC EQUATIONS

  • KIM, SEICK
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.19 no.2
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    • pp.189-195
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    • 2015
  • The goal of this note is to provide a detailed proof for local boundedness estimate near the boundary for weak solutions for second order elliptic equations with bounded measurable coefficients subject to Neumann boundary condition.

ERROR ESTIMATIES FOR A FREQUENCY-DOMAIN FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS WITH A NEUMANN BOUNDARY CONDITION

  • Lee, Jong-Woo
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.2
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    • pp.345-362
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    • 1998
  • We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

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A NUMERICAL METHOD FOR THE PROBLEM OF COEFFICIENT IDENTIFICATION OF THE WAVE EQUATION BASED ON A LOCAL OBSERVATION ON THE BOUNDARY

  • Shirota, Kenji
    • Communications of the Korean Mathematical Society
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    • v.16 no.3
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    • pp.509-518
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    • 2001
  • The purpose of this paper is to propose a numerical algorithm for the problem of coefficient identification of the scalar wave equation based on a local observation on the boundary: Determine the unknown coefficient function with the knowledge of simultaneous Dirichlet and Neumann boundary values on a part of boundary. To find the unknown coefficient function, the unknown Neumann boundary value is also identified. We recast our inverse problem to variational problem. The gradient method is applied to find the minimizing functions. We confirm the effectiveness of our algorithm by numerical experiments.

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ON EXISTENCE OF WEAK SOLUTIONS OF NEUMANN PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING p-LAPLACIAN IN AN UNBOUNDED DOMAIN

  • Hang, Trinh Thi Minh;Toan, Hoang Quoc
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.6
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    • pp.1169-1182
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    • 2011
  • In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form $$-div(h(x){\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+b(x){\mid}u{\mid}^{p-2}u=f(x,\;u),\;p{\geq}2$$ in an unbounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, with sufficiently smooth bounded boundary ${\partial}{\Omega}$, where $h(x){\in}L_{loc}^1(\overline{\Omega})$, $\overline{\Omega}={\Omega}{\cup}{\partial}{\Omega}$, $h(x){\geq}1$ for all $x{\in}{\Omega}$. The proof of main results rely essentially on the arguments of variational method.

GLOBAL SOLUTIONS FOR THE ${\bar{\partial}}$-PROBLEM ON NON PSEUDOCONVEX DOMAINS IN STEIN MANIFOLDS

  • Saber, Sayed
    • Journal of the Korean Mathematical Society
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    • v.54 no.6
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    • pp.1787-1799
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    • 2017
  • In this paper, we prove basic a priori estimate for the ${\bar{\partial}}$-Neumann problem on an annulus between two pseudoconvex submanifolds of a Stein manifold. As a corollary of the result, we obtain the global regularity for the ${\bar{\partial}}$-problem on the annulus. This is a manifold version of the previous results on pseudoconvex domains.

DIRECT DETERMINATION OF THE DERIVATIVES OF CONDUCTIVITY AT THE BOUNDARY FROM THE LOCALIZED DIRICHLET TO NEUMANN MAP

  • Gen-Nakamura;Kazumi-Tanuma
    • Communications of the Korean Mathematical Society
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    • v.16 no.3
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    • pp.415-425
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    • 2001
  • We consider the problem of determining conductivity of the medium from the measurements of the electric potential on the boundary and the corresponding current flux across the boundary. We give a formula for reconstructing the conductivity and its normal derivative at the point of the boundary simultaneously from the localized Diichlet to Neumann map around that point.

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THREE SOLUTIONS TO A CLASS OF NEUMANN DOUBLY EIGENVALUE ELLIPTIC SYSTEMS DRIVEN BY A (p1,...,pn)-LAPLACIAN

  • Afrouzi, Ghasem A.;Heidarkhani, Shapour;O'Regan, Donal
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1235-1250
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    • 2010
  • In this paper we establish the existence of at least three weak solutions for Neumann doubly eigenvalue elliptic systems driven by a ($p_1,\ldots,p_n$)-Laplacian. Our main tool is a recent three critical points theorem of B. Ricceri.