scholarly journals Inverse heat source problem for a coupled hyperbolic-parabolic system

2016 ◽  
Vol Volume 23 - 2016 - Special... ◽  
Author(s):  
Mourad Bellassoued ◽  
Bochra Riahi
Keyword(s):  
Heat Source ◽  
Parabolic System ◽  
Parabolic Type ◽  
Coupled System ◽  
Consolidation Model ◽  
International Audience ◽  
Inverse Estimation ◽  
Problème Inverse ◽  
Inverse Heat Source ◽  
Hölder Stability

International audience Dans ce papier, on a prouvé une estimation de stabilité de type Höldérienne pour un problème inverse de détermination du terme source de l'équation de la chaleur à l'aide d'une inégalité de Carleman pour un système d'équations hyperbolique-parabolique couplé. ABSTRACT. In this paper we consider a coupled system of mixed hyperbolic-parabolic type which describes the Biot consolidation model in poro-elasticity. Using a local Carleman estimate for a coupled hyperbolic-parabolic system, we prove the uniqueness and a Hölder stability in determining the heat source by a single measurement of solution over ω × (0, T), where T > 0 is a sufficiently large time and a suitable subbdomain ω ⊂ Ω such that ∂ω ⊃ ∂Ω. MOTS-CLÉS : Problème inverse, estimation de Carleman, système couplet

Inverse estimation of location of internal heat source in conduction

2011 ◽  
Vol 19 (3) ◽  
pp. 337-361 ◽  
Author(s):  
S. Ghosh ◽  
D.K. Pratihar ◽  
B. Maiti ◽  
P.K. Das
Keyword(s):  
Heat Source ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Inverse Estimation

scholarly journals The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics

1996 ◽  
Vol 1 (2) ◽  
pp. 203-217 ◽  
Author(s):  
George Avalos
Keyword(s):  
Wave Equation ◽  
Feedback Control ◽  
Exponential Stability ◽  
Parabolic System ◽  
Hyperbolic Equations ◽  
Coupled System ◽  
Beam Equation ◽  
Structural Acoustics ◽  
Uniform Stabilization ◽  
Structure Interaction

We show here the uniform stabilization of a coupled system of hyperbolic and parabolic PDE's which describes a particular fluid/structure interaction system. This system has the wave equation, which is satisfied on the interior of a bounded domainΩ, coupled to a “parabolic–like” beam equation holding on∂Ω, and wherein the coupling is accomplished through velocity terms on the boundary. Our result is an analog of a recent result by Lasiecka and Triggiani which shows the exponential stability of the wave equation via Neumann feedback control, and like that work, depends upon a trace regularity estimate for solutions of hyperbolic equations.

scholarly journals The physical and qualitative analysis of fluctuations in air and vapour concentrations in a porous medium

2018 ◽  
Vol 5 (5) ◽  
pp. 171954 ◽  
Author(s):  
Y. Poorun ◽  
M. Z. Dauhoo ◽  
M. Bessafi ◽  
M. K. Elahee ◽  
A. Gopaul ◽  
...  
Keyword(s):  
Transport Model ◽  
Parabolic Type ◽  
Coupled System ◽  
Numerical Approach ◽  
The Body ◽  
Physical Analysis ◽  
System Of Equations ◽  
Ambient Conditions ◽  
Singular Coefficient ◽  
Transport Diffusion

This work presents the development and physical analysis of a sweat transport model that couples the fluctuations in air and vapour concentrations, and temperature, in a one-dimensional porous clothing assembly. The clothing is exposed to inherent time-varying conditions due to variations in the body temperature and ambient conditions. These fluctuations are governed by a coupled system of nonlinear relaxation–transport–diffusion PDEs of Petrovskii parabolic type. A condition for the well-posedness of the resulting system of equations is derived. It is shown that the energy of the diffusion part of the system is exponentially decreasing. The boundedness and stability of the system of equations is thus confirmed. The variational formulation of the system is derived, and the existence and uniqueness of a weak solution is demonstrated analytically. This system is shown to conserve positivity. The difficulty of obtaining an analytical solution due to the complexity of the problem, urges for a numerical approach. A comparison of three cases is made using the Crank–Nicolson finite difference method (FDM). Numerical experiments show the existence of singular coefficient matrices at the site of phase change. Furthermore, the steady-state profiles of temperature, air and vapour concentrations influence the attenuation of fluctuations. Numerical results verify the analytical findings of this work.

OPTIMAL ERROR BOUND AND A GENERALIZED TIKHONOV REGULARIZATION METHOD FOR IDENTIFYING AN UNKNOWN SOURCE IN THE POISSON EQUATION

2013 ◽  
Vol 12 (01) ◽  
pp. 1450004
Author(s):  
AI-LIN QIAN ◽  
JIAN-FENG MAO
Keyword(s):  
Heat Source ◽  
Numerical Experiment ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Stability Estimate ◽  
Tikhonov Regularization Method ◽  
Optimal Error ◽  
The Poisson Equation ◽  
Optimal Error Bound ◽  
Inverse Heat Source

In this note we prove a stability estimate for an inverse heat source problem. Based on the obtained stability estimate, we present a generalized Tikhonov regularization method and obtain the error estimate. Numerical experiment shows that the generalized Tikhonov regularization works well.

scholarly journals Inverse Heat Source Problem and Experimental Design for Determining Iron Loss Distribution

2021 ◽  
Vol 43 (2) ◽  
pp. B243-B270
Author(s):  
Antti Hannukainen ◽  
Nuutti Hyvönen ◽  
Lauri Perkkiö
Keyword(s):  
Experimental Design ◽  
Heat Source ◽  
Iron Loss ◽  
Loss Distribution ◽  
Inverse Heat Source
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