Results 51 to 60 of about 413,861 (307)
An ill posed problem for a hyperbolic equation near a corner
, 1973 The purpose of this note is to give a simple example of an ill posed problem for a hyperbolic equation to be solved in a region whose boundary has a corner. In [2] we gave necessary and sufficient conditions for existence, uniqueness, and the validity of
S. Osher
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Advanced Functional Materials, EarlyView.Atomic layer deposition is used to conformally surface engineer polymeric membranes to fabricate inorganic–organic hybrid membranes. These membranes have exceptionally strong attraction toward water even in high oil containing emulsions, which leads to an extremely strong hydration layer at the interface.
Bratin Sengupta +8 more
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Tạp chí Khoa họcIn this paper, we first prove that the heat equation backward in time with Dirichlet and integral boundary conditions is an ill- posed problem. Then, we establish a stability estimate of Hölder type for this ill-posed problem.
Nguyen Van Duc, Phan Hoai Linh
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Boundary Value Problems, 2018 In this paper, we study an inverse initial value problem for the fractional diffusion equation with discrete noise. This problem is ill-posed in the sense of Hadamard.
Fan Yang +3 more
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Regularization of exponentially ill-posed problems
Numerical Functional Analysis and Optimization, 2000 Linear and nonlinear inverse problems which are exponentially ill-posed arise in heat conduction, satellite gradiometry, potential theory and scattering theory. For these problems logarithmic source conditions have natural interpretations whereas standard Holder-type source conditions are far too restrictive.
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Interaction‐Driven Assembly Pathways in Heterogeneous Active Microrobotic Systems
Advanced Functional Materials, EarlyView.Peanut‐ and cube‐shaped light‐powered microrobots exhibit distinct magnetic and photocatalytic responses that determine their heterogeneous self‐assembly. In the dark, magnetic dipole interactions drive colloidal copolymerization with cubes acting as nucleation centers, whereas under light irradiation, phoretic interactions compete with magnetic ...
Domenico Calabrò +5 more
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Spectral Regularization Methods for an Abstract Ill-Posed Elliptic Problem
Abstract and Applied Analysis, 2013 We study an abstract elliptic Cauchy problem associated with an unbounded self-adjoint positive operator which has a continuous spectrum. It is well-known that such a problem is severely ill-posed; that is, the solution does not depend continuously on ...
Nadjib Boussetila +2 more
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Open Mathematics, 2023 In this article, we investigate a spherically symmetric backward heat conduction problem, starting from the final temperature. This problem is severely ill posed: the solution (if it exists) does not depend continuously on the final data.
Cheng Wei, Liu Yi-Liang
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The residual method for regularizing ill-posed problems
Applied Mathematics and Computation, 2011 Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov regularization, where a series of new results for regularization in Banach spaces has been published in the recent years.
Markus Grasmair +2 more
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Advanced Healthcare Materials, EarlyView.Efficient recovery from traumatic or degenerative diseases is a great challenge, even after all the advancements in bone and cartilage regeneration. Machine learning (ML) algorithms have presented opportunities to enhance these aspects by accurately analyzing imaging data.
Maryam Kamaei +9 more
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