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

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.

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

Evolution Equations and Control Theory ◽

10.3934/eect.2021060 ◽

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>

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.380-384.1143 ◽

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.

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An inverse problem for a fractional diffusion equation with fractional power type nonlinearities

Inverse Problems and Imaging ◽

10.3934/ipi.2021064 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Li Li

Keyword(s):

Inverse Problem ◽

Diffusion Equation ◽

Approximation Property ◽

Fractional Power ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Well Posedness ◽

Power Type ◽

First Order ◽

Dirichlet To Neumann Map

<p style='text-indent:20px;'>We study the well-posedness of a semi-linear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map. Our arguments are based on a first order linearization as well as the parabolic Runge approximation property.</p>

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

Journal of Computational Methods in Sciences and Engineering ◽

10.3233/jcm-200034 ◽

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.

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