[PDF] Top 20 Regularization of an initial inverse problem for a biharmonic equation

... The paper is organized as follows. In Sect. 2, the formulation of the problem and its ill- posed property are given. In Sect. 3, stability estimates are proved under a priori condi- tions on the solution. ... See full document

... control problem for indicated variational in- equality has a non-empty feasible set and this problem is always ...original problem can be attained in the limit by optimal solutions of the penalized ... See full document

... where ε > 0 is the noise level (in this paper we will also let · denote the L 2 (Ω) norm). We show that this problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the given ... See full document

... direct problem using the Laplace ...our inverse problem is reduced to the integral equation of Volterra type; then we apply the Tikhonov regularization method to compute the boundary ... See full document

... advection–dispersion equation [18]. However, the advection–dispersion equation is not suitable for anomalous diffusion, ...advection–dispersion equation by a generalized derivative of order α with 0 ... See full document

... Cauchy problem for Helmholtz equation arises from inverse scattering ...this problem are ...Tikhonov regularization, and singular value decomposition methods are compared in ...Cauchy ... See full document

... Cauchy problem and the general inverse boundary value problem in static planar ther- moelasticity have recently been addressed by Marin and Karageorghis [34], and Karageorghis et ...non-iterative ... See full document

... The diffusion may be one of the most important and attractive notions in mathe- matical methods for image analysis. Diffusion equation is one of the most important models which appears in the MRI, and often is ... See full document

... Several regularization procedures have been developed to solve such ill-conditioned system, see for example Hansen ...used regularization technique is the Tikhonov regularization method ... See full document

... an inverse problem to determine a source term in the parabolic equation, once the measured data are obtained at a later ...this problem is ill-posed, therefore the Tikhonov ... See full document

... the inverse time problem for the axisymmetric heat equation which is a severely ill-posed ...two regularization parameters, one related to the error in measurement process and the other ... See full document

... Black-Scholes equation, it is necessary to accurately measure it in portfolio selection, underlying financial products pricing and hedging or risk ...an inverse problem with the final observation, and ... See full document

... known initial-boundary ...the initial condition because the heat process has al- ready started before we estimate the ...without initial value [, ...quasi-reversibility regularization method ... See full document

... In the past, many approaches have been studied for solving ill-posed problems, espe- cially the backward heat problems. For example, Lattès and Lions [], Showalter [] and Boussetila and Rebbani [] used the ... See full document

... In this section, we introduce the trigonometric method in nonparametric regression asso- ciated with quasi-boundary value regularization method to solve the inverse initial value problem of a ... See full document

... ill-posed problem into a family of well-posed fourth-order problems that depend on a regularization parameter ...of inverse problems such as inverse heat conduction problem [, ], ... See full document

... an inverse initial value problem of the biparabolic equation; this problem is ill-posed and the regularization methods are needed to stabilize the numerical ...modified ... See full document

... of inverse problems such as the IHCP [], the Cauchy problem of Laplace equation [, ], the backward heat conduction problem [], the inverse source identification problems [, ] ... See full document

... The problem of identification of a coefficient in a nonlinear parabolic equation is an interesting problem for many scientists ...[–]. Inverse problems for parabolic equations with nonlocal ... See full document

... The second section is devoted to physical model and presentation of the mathematical formulation of the boundary detection problem. In section 3; we formulate the problem in a shape optimization ... See full document