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Approximate Solution of Inverse Problem for Elliptic Equation with Overdetermination [PDF]
Abstract and Applied Analysis, 2013 A finite difference method for the approximate solution of the inverse problem for the multidimensional elliptic equation with overdetermination is applied.
Charyyar Ashyralyyev, Mutlu Dedeturk
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Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem [PDF]
SIAM Journal on Numerical Analysis, 2011 We consider the inverse problem of determining the permeability from the pressure in a Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion coefficient for a linear uniformly elliptic partial differential equation in divergence form, in a bounded domain in dimension $d \le 3$, from measurements of the solution in ...
Andrew Stuart
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Uniqueness of semilinear elliptic inverse problem
International Journal of Mathematics and Mathematical Sciences, 2003 We consider the uniqueness of the inverse problem for a semilinear elliptic differential equation with Dirichlet condition. The necessary and sufficient condition of unique solution is obtained.
Chaochun Qu, Ping Wang
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On an Inverse Problem for Quasi-Linear Elliptic Equation [PDF]
Journal of Siberian Federal University - Mathematics and Physics, 2015 Summary: The identification of an unknown constant coefficient in the main term of the partial differential equation \(- kM\psi(u) + g(x) u = f(x)\) with the Dirichlet boundary condition is investigated. Here \(\psi(u)\) is a nonlinear increasing function of \(u, M\) is a linear self-adjoint elliptic operator of the second order.
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Cumhuriyet Science Journal, 2020 An inverse boundary value problem for a second-order elliptic equation with periodic and integral condition is investigated. The problem is considered in a rectangular domain.
Nergiz Heydarzade +2 more
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Kernel Methods for Bayesian Elliptic Inverse Problems on Manifolds [PDF]
SIAM/ASA Journal on Uncertainty Quantification, 2020 This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the diffusion coefficient of a second-order elliptic PDE on a closed manifold from noisy measurements of the solution ...
John Harlim +2 more
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Boundary value problem for mixed type equation of the third order with periodic conditions
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013 The problem for the equation of the mixed elliptic-hyperbolic type with nonlocal boundary conditions is viewed. This problem is reduced to the inverse problem for elliptic-hyperbolic equation with unknown right-hand parts. The criterion of the uniqueness
G. Yu. Udalova, K. B. Sabitov
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Boundary Value Problems, 2006 Via the linking theorem, the existence of nontrivial solutions for a nonlinear elliptic Dirichlet boundary value problem with an inverse square potential is proved.
Yongqing Li, Shenghua Weng
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Iterative regularization for elliptic inverse problems
Computers & Mathematics with Applications, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Akhtar A. Khan, Behzad Djafari Rouhani
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Cumhuriyet Science Journal, 2019 An inverse boundary value problem for asecond-order elliptic equation with periodic and integral condition isinvestigated. The definition of a classical solution of the problem isintroduced.
N.a. Heydarzade +2 more
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