Results 21 to 30 of about 2,916,443 (230)
A nonhomogeneous backward heat problem: Regularization and error estimates [PDF]
Electronic Journal of Differential Equations, 2008 We consider the problem of finding the initial temperature, from the final temperature, in the nonhomogeneous heat equation $$displaylines{ u_t-u_{xx}= f(x,t),quad (x,t)in (0,pi)imes (0,T),\ u(0,t)= u(pi,t)= 0, quad (x,t) in (0,pi)imes(0,T ...
Trong Dang Duc, Huy Tuan Nguyen
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Lipschitz Stability for Backward Heat Equation with Application to Fluorescence Microscopy [PDF]
SIAM Journal on Mathematical Analysis, 2021 In this work we study a Lipschitz stability result in the reconstruction of a compactly supported initial temperature for the heat equation in ${\mathbb{R}}^n$, from measurements along a positive time interval and over an open set containing its support. We employ a nonconstructive method which ensures the existence of the stability constant, but it is
Pablo Arratia +4 more
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On the Stability of a Forward–Backward Heat Equation [PDF]
Integral Equations and Operator Theory, 2012 21 pages, 3 ...
Boulton, Lyonell +2 more
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, 2021 We verify strong rates of convergence for a time-implicit, finite-element based space-time discretization of the backward stochastic heat equation, and the forward-backward stochastic heat equation from stochastic optimal control.
Andreas Prohl, Yanqing Wang
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Lack of controllability of the heat equation with memory [PDF]
, 2012 We consider a model for the heat equation with memory, which has infinite propagation speed, like the standard heat equation. We prove that, in spite of this, for every T > 0 there exist square integrable initial data which cannot be steered to hit zero ...
Andrei Halanay, Pandolfi, Luciano
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Backward stochastic partial differential equations driven by infinite-dimensional martingales and applications [PDF]
, 2009 This paper studies first a result of existence and uniqueness of the solution to a backward stochastic differential equation driven by an infinite-dimensional martingale.
Al-Hussein, AbdulRahman +1 more
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On the Nature of Ill-Posedness of the Forward-Backward Heat Equation [PDF]
Integral Equations and Operator Theory, 2009 We study the Cauchy problem with periodic initial data for the forward-backward heat equation defined by the J-self-adjoint linear operator L depending on a small parameter. The problem has been originated from the lubrication approximation of a viscous fluid film on the inner surface of the rotating cylinder.
Chugunova, Marina +2 more
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On Optimal Regularization Methods for the Backward Heat Equation
Zeitschrift für Analysis und ihre Anwendungen, 1996 In this paper we consider different regularization methods for solving the heat equation u_1 + Au = 0 (0 ≤ t < T) backward in time, where A : H \to H is a linear (
Tautenhahn, U., Schröter, T.
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Regularization of the backward stochastic heat conduction problem [PDF]
, 2021 In this paper, we study the backward problem for the stochastic parabolic heat equation driven by a Wiener process. We show that the problem is ill-posed by violating the continuous dependence on the input data.
Huy Tuan, N +7 more
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Regularity for some backward heat equations [PDF]
Journal of Physics A: Mathematical and Theoretical, 2010 We study boundary value problems for backward parabolic heat equations with the Cauchy condition at the initial time, i.e. at the 'wrong' end of the time interval. We found that existence, uniqueness and regularity of solutions can still be achieved for the problem with boundary inputs.
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