Results 21 to 30 of about 94,152 (277)
Inverse Numerical Range and Determinantal Quartic Curves
Mathematics, 2020 A hyperbolic ternary form, according to the Helton–Vinnikov theorem, admits a determinantal representation of a linear symmetric matrix pencil. A kernel vector function of the linear symmetric matrix pencil is a solution to the inverse numerical range ...
Mao-Ting Chien, Hiroshi Nakazato
doaj +1 more source
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
openaire +2 more sources
Approximation of mild solutions of the linear and nonlinear elliptic equations [PDF]
, 2014 In this paper, we investigate the Cauchy problem for both linear and semi-linear elliptic equations. In general, the equations have the form \[ \frac{\partial^{2}}{\partial t^{2}}u\left(t\right)=\mathcal{A}u\left(t\right)+f\left(t,u\left(t\right)\right)
Dang Duc Trong +4 more
core +1 more source
Inverse coefficient problems for nonlinear elliptic equations [PDF]
The ANZIAM Journal, 2007 AbstractThis paper is devoted to a class of inverse coefficient problems for nonlinear elliptic equations. The unknown coefficient of the elliptic equations depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic equations are uniquely solvable for the given class of coefficients.
Yang, Runsheng, Ou, Yunhua
openaire +1 more source
Identification of discontinuous parameters in double phase obstacle problems
Advances in Nonlinear Analysis, 2022 In this article, we investigate the inverse problem of identification of a discontinuous parameter and a discontinuous boundary datum to an elliptic inclusion problem involving a double phase differential operator, a multivalued convection term (a ...
Zeng Shengda +3 more
doaj +1 more source
On efficient quantum block encoding of pseudo-differential operators [PDF]
Quantum, 2023 Block encoding lies at the core of many existing quantum algorithms. Meanwhile, efficient and explicit block encodings of dense operators are commonly acknowledged as a challenging problem.
Haoya Li, Hongkang Ni, Lexing Ying
doaj +1 more source
A new approach to nonlinear constrained Tikhonov regularization [PDF]
, 2011 We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of the forward ...
Ito, Kazufumi, Jin, Bangti
core +1 more source
Inverse Coefficient Problem for Elliptic Hemivariational Inequality
, 2001 In this paper we consider the problem of identification of a discontinuous coefficient in elliptic hemivariational inequality. First we prove an existence theorem for an inverse problem and we establish the boundary homogenization result for the direct problem. Then we study the asymptotic behavior of the set of solutions to the inverse problem.
Migórski, Stanisław, Ochal, Anna
openaire +2 more sources
Mathematics, 2022 Inverse problems of recovering surface fluxes on the boundary of a domain from pointwise observations are considered. Sharp conditions on the data ensuring existence and uniqueness of solutions in Sobolev classes are exposed.
Sergey Pyatkov, Denis Shilenkov
doaj +1 more source
Survivals of two cooperating species of animals
Partial Differential Equations in Applied Mathematics, 2021 The purpose of this paper is to give conditions for the existence and uniqueness of positive solution to a rather general type of elliptic system of the Dirichlet problem on a bounded domain Ω in Rn.
Joon Hyuk Kang
doaj +1 more source