243,398 research outputs found
Simultaneous determination of time-dependent coefficients and heat source
This article presents a numerical solution to the inverse problems of simultaneous determination of the time-dependent coefficients and the source term in the parabolic heat equation subject to overspecified conditions of integral type. The ill-posed problems are numerically discretized using the finite-difference method. The resulting system of nonlinear equations is solved numerically using the MATLAB toolbox routine lsqnonlin applied to minimizing the nonlinear Tikhonov regularization functional subject to simple physical bounds on the variables. Numerical examples are presented to illustrate the accuracy and stability of the solution
Recovery of a space-dependent vector source in thermoelastic systems
In this contribution, an inverse problem of determining a space-dependent vector source in a thermoelastic system of type-I, type-II and type-III is studied using information from a supplementary measurement at a fixed time. These thermoelastic systems consist of two equations that are coupled: a parabolic equation for the temperature
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and a vectorial hyperbolic equation for the displacement
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. In this latter one, the source is unknown, but solely space dependent. A spacewise-dependent additional measurement at the final time ensures that the inverse problem corresponding with each type of thermoelasticity has a unique solution when a damping term
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(with
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componentwise strictly monotone increasing) is present in the hyperbolic equation. Despite the ill-posed nature of these inverse problems, a stable iterative algorithm is proposed to recover the unknown source in the case that
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is also linear. This method is based on a sequence of well-posed direct problems, which are numerically solved at each iteration, step by step, using the finite element method. The instability of the inverse source problem is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results support the theoretically obtained results
Thermal recoil force, telemetry, and the Pioneer anomaly
Precision navigation of spacecraft requires accurate knowledge of small
forces, including the recoil force due to anisotropies of thermal radiation
emitted by spacecraft systems. We develop a formalism to derive the thermal
recoil force from the basic principles of radiative heat exchange and
energy-momentum conservation. The thermal power emitted by the spacecraft can
be computed from engineering data obtained from flight telemetry, which yields
a practical approach to incorporate the thermal recoil force into precision
spacecraft navigation. Alternatively, orbit determination can be used to
estimate the contribution of the thermal recoil force. We apply this approach
to the Pioneer anomaly using a simulated Pioneer 10 Doppler data set.Comment: 10 pages, 3 figures. Published versio
Inverse source problems for degenerate time-fractional PDE
In this paper, we investigate two inverse source problems for degenerate
time-fractional partial differential equation in rectangular domains. The first
problem involves a space-degenerate partial differential equation and the
second one involves a time-degenerate partial differential equation. Solutions
to both problem are expressed in series expansions. For the first problem, we
obtained solutions in the form of Fourier-Legendre series. Convergence and
uniqueness of solutions have been discussed. Solutions to the second problem
are expressed in the form of Fourier-Sine series and they involve a generalized
Mittag- Leffler type function. Moreover, we have established a new estimate for
this generalized Mittag-Leffler type function. The obtained results are
illustrated by providing example solutions using certain given data at the
initial and final time.Comment: 12 pages, 8 figure
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