scholarly journals Stability estimate for a partial data inverse problem for the convection-diffusion equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Soumen Senapati ◽  
Manmohan Vashisth
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Stability Estimate ◽  
Convection Term ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Gauge Term ◽  
Boundary Measurements ◽  
The Stability ◽  
Density Coefficient

<p style='text-indent:20px;'>In this article, we study the stability in the inverse problem of determining the time-dependent convection term and density coefficient appearing in the convection-diffusion equation, from partial boundary measurements. For dimension <inline-formula><tex-math id="M1">\begin{document}$ n\ge 2 $\end{document}</tex-math></inline-formula>, we show the convection term (modulo the gauge term) admits log-log stability, whereas log-log-log stability estimate is obtained for the density coefficient.</p>

Stability estimate for an inverse problem of the convection-diffusion equation

2020 ◽  
Vol 28 (1) ◽  
pp. 71-92
Author(s):  
Mourad Bellassoued ◽  
Imen Rassas
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Scalar Potential ◽  
Stability Estimate ◽  
Inverse Boundary ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
First Order ◽  
Order Coefficient ◽  
Dirichlet To Neumann Map

AbstractWe consider the inverse boundary value problem for the dynamical steady-state convection-diffusion equation. We prove that the first-order coefficient and the scalar potential are uniquely determined by the Dirichlet-to-Neumann map. More precisely, we show in dimension {n\geq 3} a log-type stability estimate for the inverse problem under consideration. The method is based on reducing our problem to an auxiliary inverse problem and the construction of complex geometrical optics solutions of this problem.

The Best Perturbation Method for the Parameter Inversion of Two-Dimension Convection-Diffusion Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1143-1146
Author(s):  
Xiang Guo Liu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Parameter Inversion ◽  
Parametric Inversion

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

Approximation of 3D convection diffusion equation using DQM based on modified cubic trigonometric B-splines

2020 ◽  
pp. 1-10
Author(s):  
Mohammad Tamsir ◽  
Neeraj Dhiman ◽  
F.S. Gill ◽  
Robin
Keyword(s):  
Diffusion Equation ◽  
Numerical Solutions ◽  
Basis Functions ◽  
B Spline ◽  
Convection Diffusion ◽  
B Splines ◽  
Convection Diffusion Equation ◽  
First Order ◽  
The Stability ◽  
Derivatives Of

This paper presents an approximate solution of 3D convection diffusion equation (CDE) using DQM based on modified cubic trigonometric B-spline (CTB) basis functions. The DQM based on CTB basis functions are used to integrate the derivatives of space variables which transformed the CDE into the system of first order ODEs. The resultant system of ODEs is solved using SSPRK (5,4) method. The solutions are approximated numerically and also presented graphically. The accuracy and efficiency of the method is validated by comparing the solutions with existing numerical solutions. The stability analysis of the method is also carried out.

Filtering for the Inverse Problem of Convection–Diffusion Equation with a Point Source

2012 ◽  
Vol 81 (11) ◽  
pp. 114401 ◽  
Author(s):  
Fujihiro Hamba ◽  
Satoshi Abe ◽  
Daisuke Kitazawa ◽  
Shinsuke Kato
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Point Source ◽  
Convection Diffusion ◽  
Convection Diffusion Equation

scholarly journals A partial data inverse problem for the convection-diffusion equation

2020 ◽  
Vol 14 (1) ◽  
pp. 53-75
Author(s):  
Suman Kumar Sahoo ◽  
◽  
Manmohan Vashisth ◽  
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Partial Data

The approximate solutions to source inverse problem of 1-D convection–diffusion equation by LS-SVM

2017 ◽  
Vol 26 (5) ◽  
pp. 677-690 ◽  
Author(s):  
Jiaju Yu ◽  
Fule Li ◽  
Shuanghe Yu ◽  
Ziku Wu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Approximate Solutions ◽  
Convection Diffusion ◽  
Convection Diffusion Equation

scholarly journals Difference scheme for the convection-diffusion equation of fractional order

2021 ◽  
pp. 146-154
Author(s):  
Е.М. Казакова
Keyword(s):  
Diffusion Equation ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Fractional Order ◽  
Boundary Value ◽  
Stability And Convergence ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The Difference ◽  
The Stability

Построена разностная схема, аппроксимирующая первую краевую задачу для уравнения конвекции-диффузии дробного порядка с постоянными коэффициентами. Исследована устойчивость и сходимость разностной схемы. A difference scheme is constructed that approximates the first boundary value problem for the fractional-order convection-diffusion equation. The stability and convergence of the difference scheme.

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