Results 71 to 80 of about 676,988 (164)

Ill-posedness for the Zakharov system with generalized nonlinearity

, 2015
We study the ill-posedness question for the one-dimensional Zakharov system and a generalization of it in one and higher dimensions. Our point of reference is the criticality criteria introduced by Ginibre, Tsutsumi and Velo (1997) to establish local ...
Linares, F, Biagioni, HA
core   +2 more sources

Well-posed Vector Optimization Problems and Vector Variational Inequalities [PDF]

In this paper we introduce notions of well-posedness for a vector optimization problem and for a vector variational inequality of differential type, we study their basic properties and we establish the links among them.
Rocca Matteo
core  

An inverse problem in a parabolic equation

Electronic Journal of Differential Equations, 1998
In this paper, an inverse problem in a parabolic equation is studied. An unknown function in the equation is related to two integral equations in terms of heat kernel. One of the integral equations is well-posed while another is ill-posed.
Zhilin Li, Kewang Zheng
doaj  

Sparse Rational Polynomial Coefficient Estimation Method via Low-Rank Matrix Constraint

Remote Sensing
The rational function model (RFM) is an important general imaging model in remote sensing image geometric processing, which is composed of many rational polynomial coefficients (RPCs). However, due to the correlation among the high-order polynomials, the
Congzhen Hu, Jiajie He, Tianyu Yan, Pu Wang, Wei An, Yingqian Wang   +5 more
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Comparative Analysis of Methods for Regularizing an Initial Boundary Value Problem for the Helmholtz Equation

Journal of Applied Mathematics, 2014
We consider an ill-posed initial boundary value problem for the Helmholtz equation. This problem is reduced to the inverse continuation problem for the Helmholtz equation.
Sergey Igorevich Kabanikhin, M. A. Shishlenin, D. B. Nurseitov, A. T. Nurseitova, S. E. Kasenov   +4 more
doaj   +1 more source

A Note on the Generalized Camassa-Holm Equation

Journal of Function Spaces, 2014
We study the generalized Camassa-Holm equation which contains the Camassa-Holm (CH) equation and Novikov equation as special cases with the periodic boundary condition.
Yun Wu, Ping Zhao
doaj   +1 more source

Research on Human Lung Impedance Tomography Based on Soft Thresholding Image Segmentation and Reduced-Order Tikhonov Regularization

Applied Sciences
The lung is one of the most vital organs in the human body, and its condition is closely correlated with overall health. Electrical impedance tomography (EIT), as a biomedical imaging technique, often produces low-quality reconstructed images due to its ...
Yang Song, Lan Xiong, Zhenyou Liu, Yongye Wu, Zhanlong Zhang   +4 more
doaj   +1 more source

Measuring Residual Stresses with Crack Compliance Methods: An Ill-Posed Inverse Problem with a Closed-Form Kernel

Applied Mechanics
By means of relaxation methods, residual stresses can be obtained by introducing a progressive cut or a hole in a specimen and by measuring and elaborating the strains or displacements that are consequently produced.
Marco Beghini, Tommaso Grossi
doaj   +1 more source

An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales

International Journal of Mathematics and Mathematical Sciences, 2003
Recently, Tautenhahn and Hämarik (1999) have considered a monotone rule as a parameter choice strategy for choosing the regularization parameter while considering approximate solution of an ill-posed operator equation Tx=y, where T is a bounded linear ...
Santhosh George, M. Thamban Nair
doaj   +1 more source

Local ill-posedness of the 1D Zakharov system

Electronic Journal of Differential Equations, 2007
Ginibre-Tsutsumi-Velo (1997) proved local well-posedness for the Zakharov system$$displaylines{ ipartial_tu + Delta u = nu cr partial_t^2 n - Delta n = Delta |u|^2 cr u(x,0)=u_0(x), cr n(x,0)=n_0(x), quad partial_tn(x,0)=n_1(x)}$$ where $u=u(x,t)in ...
Justin Holmer
doaj