Results 1 to 10 of about 6,390,993 (306)
A Strongly Ill-Posed Problem for the Equation
Cumhuriyet Science Journal, 2018 In this work, we consider an inverse problem for an elliptic equationwhich is strongly ill-posed in Hadamard sense. We prove the uniqueness of thesolution of the problem by using Carleman estimates.
Mustafa Yıldız
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A modified quasi-boundary value method for an abstract ill-posed biparabolic problem
Open Mathematics, 2017 In this paper, we are concerned with the problem of approximating a solution of an ill-posed biparabolic problem in the abstract setting. In order to overcome the instability of the original problem, we propose a modified quasi-boundary value method to ...
Besma Khelili +2 more
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On a time fractional diffusion with nonlocal in time conditions
Advances in Difference Equations, 2021 In this work, we consider a fractional diffusion equation with nonlocal integral condition. We give a form of the mild solution under the expression of Fourier series which contains some Mittag-Leffler functions. We present two new results.
Nguyen Hoang Tuan +3 more
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Approximation of inverse source problem for time fractional pseudo-parabolic equation in $L^p$ [PDF]
Mathematics and Computational Sciences, 2023 In this work, we focus on the final value problem of an inverse problem for the pseudo-parabolic equation. This study aims to provide a regularization method for this equation, once the measurement data are obtained at the final time in $L^{r}(0,\pi ...
Phong Tran, Long Le
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Updating the Landweber Iteration Method for Solving Inverse Problems
Mathematics, 2022 The Landweber iteration method is one of the most popular methods for the solution of linear discrete ill-posed problems. The diversity of physical problems and the diversity of operators that result from them leads us to think about updating the main ...
Hassan K. Ibrahim Al-Mahdawi +4 more
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Regularization and Error Estimate for the Poisson Equation with Discrete Data
Mathematics, 2019 In this work, we focus on the Cauchy problem for the Poisson equation in the two dimensional domain, where the initial data is disturbed by random noise.
Nguyen Anh Triet +3 more
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Ill-posed problems in thermomechanics
Applied Mathematics Letters, 2009 Several thermomechanical models have been proposed from a heuristic point of view. A mathematical analysis should help to clarify the applicability of these models, among those recent thermal or viscoelastic models. Single-phase-lag and dual-phase-lag heat conduction models can be interpreted as formal expansions of delay equations. The delay equations
Michael Dreher +2 more
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Viscoelastic Modulus Reconstruction Using Time Harmonic Vibrations
Mathematical Modelling and Analysis, 2015 This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the Frechet derivatives of
Habib Ammari +2 more
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The ill-posed Cauchy problem by Controllability the elliptic case
Results in Control and Optimization, 2023 In this paper, we are dealing with the ill-posed Cauchy problem for an elliptic operator. To do this, we interpret the problem as an inverse problem, and therefore a controllability problem.
Bylli André Guel, Ousseynou Nakoulima
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On Tikhonov's Method for Ill-Posed Problems [PDF]
Mathematics of Computation, 1974 For Tikhonov’s regularization of ill-posed linear integral equations, numerical accuracy is estimated by a modulus of convergence, for which upper and lower bounds are obtained. Applications are made to the backward heat equation, to harmonic continuation, and to numerical differentiation.
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