Results 1 to 10 of about 82,072,160 (134)
On Bayesian data assimilation for PDEs with ill-posed forward problems [PDF]
Inverse Problems, 2022 Abstract We study Bayesian data assimilation (filtering) for time-evolution Partial differential equations (PDEs), for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Navier–Stokes equations of fluid dynamics, are characterized by a high sensitivity of solutions to perturbations of the
S Lanthaler, S Mishra, F Weber
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Carleman weight functions for a globally convergent numerical method for ill-posed Cauchy problems for some quasilinear PDEs [PDF]
Nonlinear Analysis: Real World Applications, 2017 29 Pages, 4 ...
Michael Klibanov, Nikolay Koshev
exaly +3 more sources
Mathematical and Computational Applications, 2023 Physics-Informed Neural Networks (PINNs) are a new class of machine learning algorithms that are capable of accurately solving complex partial differential equations (PDEs) without training data.
Jacques Francois Du Toit, Ryno Laubscher
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Well-Posed and Ill-Posed Boundary Value Problems for PDE 2013 [PDF]
Abstract and Applied Analysis, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Allaberen Ashyralyev +5 more
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On iterative methods for solving ill-posed problems modeled by PDE's
CoRR, 2020 14 pages, 3 ...
Johann Baumeister, Antonio Leitão
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A General Method for the Solution of Inverse Problems in Transport Phenomena
Chemical Engineering Transactions, 2015 The typical inverse problems in transport phenomena are given by partial differential equations with unknown boundary conditions, which are to be estimated from measurements corresponding to solutions of the PDEs or of their gradients.
M. Vocciante, A. Reverberi, V. Dovi
doaj +1 more source
Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation
Numerical Functional Analysis and Optimization, 2013 The focus of this article is on conditional stability estimates for ill-posed inverse problems in partial differential equations. Conditional stability estimates have been obtained in related literature by a couple different methods. In this article, we propose a method called interpolation method, which is based on interpolation in variable Hilbert ...
Tautenhahn, Ulrich +3 more
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Operational calculus approach to PDE arising in QR-regularisation of ill-posed problems
Mathematical and Computer Modelling, 2002 The authors treat two kinds of problems using operational calculus intended for boundary value problems: the first for the backward heat equation, and the second for a nonparabolic evolution equation. They discuss the algebraization of the boundary value problem using the Duhamel principle and obtain their solution in closed form.
Dimovski, I. H., Kalla, S. L., Ali, I.
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SIAM Journal on Scientific Computing, 2014 The sideways parabolic equation (SPE) is a model of the problem of determining the temperature on the surface of a body from the interior measurements. Mathematically it can be formulated as a noncharacteristic Cauchy problem for a parabolic partial differential equation. This problem is severely ill-posed in an $L_2$ setting.
Zohreh Ranjbar, Lars Eldén
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Well‐Posed and Ill‐Posed Boundary Value Problems for PDE [PDF]
Abstract and Applied Analysis, 2012 Ashyralyev, Allaberen +4 more
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