Results 271 to 280 of about 4,839,506 (299)

Error Bounds in the Final Value Problem for the Heat Equation

SIAM Journal on Mathematical Analysis, 1976
Consider the following problem. Given the positive constants $\delta $, M, T and $f(x)$ in $L^2 (\Omega )$, find all solutions of $u_t = \Delta u$ in $\Omega \times (0,T]$, $u = 0$ on $\partial \Omega \times (0,T]$, such that $\| {u( \cdot ,T) - f} \|_{L^2 } \leqq \delta $, $\| {u( \cdot ,0) - f} \|_{L^2 } \leqq M$.
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The final value problem

1987
One of the classical ill-posed problems (in the sense of Hadamard) is the final value problem for evolution equations; a special case of this problem is the solution of the heat equation backwards in time. We consider some regularization methods for this ill-posed problem.
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Regularity of the solution for a final value problem for the Rayleigh‐Stokes equation

Mathematical Methods in the Applied Sciences, 2019
In this paper, we deal with the backward problem of determining initial condition for Rayleigh‐Stokes where the data are given at a fixed time. The problem has many applications in some non‐Newtonian fluids. We give some regularity properties of the solution to backward problem.
Hoang Luc Nguyen, Huy Tuan Nguyen, Yong Zhou   +2 more
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Generalized Tikhonov method for the final value problem of time-fractional diffusion equation

International Journal of Computer Mathematics, 2015
This paper investigates the final value problem for a time-fractional diffusion equation. We determine the initial data from a noisy final data. A generalized Tikhonov regularization method is proposed to deal with this ill-posed problem, and then the convergence rates is derived by the a-priori and a-posteriori choice rules of regularization parameter.
Hongwu Zhang, Xiaoju Zhang
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On a final value problem for fractional reaction‐diffusion equation with Riemann‐Liouville fractional derivative

Mathematical Methods in the Applied Sciences, 2019
In this paper, we study a backward problem for a fractional diffusion equation with nonlinear source in a bounded domain. By applying the properties of Mittag‐Leffler functions and Banach fixed point theorem, we establish some results above the existence, uniqueness, and regularity of the mild solutions of the proposed problem in some suitable space ...
Ngoc Tran, Vo Van Au, Yong Zhou, Nguyen Huy Tuan   +3 more
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On a final value problem for the time-fractional diffusion equation with inhomogeneous source

Inverse Problems in Science and Engineering, 2016
In this paper, we consider an inverse problem for the time-fractional diffusion equation with inhomogeneous source to determine an initial data from the observation data provided at a later time. In general, this problem is ill-posed, therefore we construct a regularizing solution using the quasi-boundary value method.
Nguyen Huy Tuan, Le Dinh Long, Van Thinh Nguyen, Thanh Tran   +3 more
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Final value optimal stochastic control problem with bounded controller.

AIAA Journal, 1967
van Gelder, A., Dunn, J., Mendelsohn, J.
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Regularization of the Final Value Problem for the Time-Fractional Diffusion Equation

Iranian Journal of Science, 2023
Mohammad F. Al-Jamal, Kamal Barghout, Nidal Abu-Libdeh   +2 more
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On a final value problem for a biparabolic equation with statistical discrete data

Applicable Analysis, 2021
Nguyen Huu Can
exaly  

Erratum to "The Final Value Problem for Sobolev Equations"

Proceedings of the American Mathematical Society, 1977
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