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Quasireversibility methods for non-well-posed problems
Published 1994-11-01“…One approach to dealing with this has been the method of quasireversibility, where the operator is perturbed to obtain a well-posed problem which approximates the original problem. …”
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Well-posed problems for the Laplace-Beltrami operator on a punctured two-dimensional sphere
Published 2023-07-01Subjects: Get full text
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On a time fractional diffusion with nonlocal in time conditions
Published 2021-04-01Subjects: Get full text
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Well-posedness, bornologies, and the structure of metric spaces
Published 2009-04-01Subjects: “…Well-posed problem…”
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ОБ УСТОЙЧИВОСТИ КРАЕВОЙ ЗАДАЧИ ДЛЯ УРАВНЕНИЯ ЧЕТНОГО ПОРЯДКА
Published 2015-06-01Subjects: Get full text
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Задача Коши для нагруженного линейного уравнения с частными производными первого порядка
Published 2023-11-01Subjects: Get full text
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Regularization technique and numerical analysis of the mixed system of first and second-kind Volterra–Fredholm integral equations
Published 2019-03-01“…We will apply the regularization method to convert this mixed system (ill-posed problem) to system of the second kind Volterra–Fredholm integral equations (well-posed problem). A numerical method based on Chebyshev wavelets is suggested for solving the obtained well-posed problem, and convergence analysis of the method is discussed. …”
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Logarithmic regularization of non-autonomous non-linear ill-posed problems in Hilbert spaces
Published 2017-01-01“…We first prove continuous dependence on modeling where the solution of the original ill-posed problem is estimated by the solution of an approximate well-posed problem. Finally, we illustrate the convergence via numerical experiments in $L^2$ spaces.…”
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USING CONJUGATE GRADIENTS PROJECTION METHOD FOR SOLVING ILL-POSED PROBLEMS ON THE SPECIAL SETS
Published 2017-06-01“…A definition of well-posed problem is given. A conjugate gradients projection method and a program written in the programming language Matlab, which solve the problem on 28 special sets of correctness are briefly described. …”
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Modified quasi-reversibility method for nonautonomous semilinear problems
Published 2013-10-01“…As in recent literature focusing on linear equations, regularization is established by approximating a solution u(t) of the problem by the solution of an approximate well-posed problem. The approximate problem will be defined by one specific approximation of the operator A(t,D) which extends a recently introduced, modified quasi-reversibility method by Boussetila and Rebbani. …”
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Continuous dependence of solutions for ill-posed evolution problems
Published 2010-09-01“…Specifically, given a positive self-adjoint operator D in a Hilbert space, we consider the ill-posed evolution problem $$displaylines{ frac{du(t)}{dt} = A(t,D)u(t) quad 0leq t<T cr u(0) = chi. }$$ We determine functions $f:[0,T]imes [0,infty)o mathbb{R}$ for which solutions of the well-posed problem $$displaylines{ frac{dv(t)}{dt} = f(t,D)v(t) quad 0leq t<T cr v(0) = chi }$$ approximate known solutions of the original ill-posed problem, thereby establishing continuous dependence on modelling for the problems under consideration.…”
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Modified Quasi Boundary Value method for inverse source biparabolic
Published 2020-07-01“…Base on this method, we give a regularized solution and we show that the regularized solution satisfies the conditions of the well-posed problem in the sense of Hadarmad. In addition, we present the estimation between the regularized solution and the sought solution by using a priori regularization parameter choice rule.…”
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Nonautonomous ill-posed evolution problems with strongly elliptic differential operators
Published 2013-04-01“…In particular, we prove the existence of a family of regularizing operators for the problem which stems from the solution of an approximate well-posed problem. In fact, depending on whether $heta in (0,pi/4]$ or $heta in (pi/4,pi/2]$, we provide two separate approximations each yielding a regularizing family. …”
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On the Principle of Excluded Middle
Published 2011-08-01“…This principle has been criticized, and sometimes rejected, on the charge that its validity depends on presuppositions that are not, some believe, universally obtainable; in particular, that any well-posed problem is solvable. My goal here is to show that, although excluded middle does indeed rest on certain presuppositions, they do not have the character of hypotheses that may or may not be true, or matters of fact that may or may not be the case. …”
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Mathematical analysis of a viscoelastic-gravitational layered earth model for magmatic intrusion in the dynamic case
Published 2015-11-01“…As a continuation of work done previously by some of the authors, this work is concerned with the proof that the perturbed equations representing the viscoelastic-gravitational displacements resulting from body forces embedded in a layered Earth model leads to a well-posed problem even for any kind of domains, with the natural boundary and transmission conditions. …”
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On Convergence of Inexact Augmented Lagrangians for Separable and Equality Convex QCQP Problems without Constraint Qualification
Published 2017-01-01“…If the feasible set is empty and the projected gradients of the Lagrangians are forced to go to zero, then the iterates are shown to converge to the nearest well posed problem.…”
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Cloud Entropy Management System Involving a Fractional Power
Published 2015-12-01“…We discuss the existence of solutions for the system as well as the stability, utilizing the Hadamard well-posed problem. Experimental results show that the proposed method demonstrates stability and performance.…”
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