Multidimensional Inverse Problem for the System of Parabolic Equations in Unbounded Domain

2015 ◽  
Vol 1 (1) ◽  
pp. 20-30
Author(s):  
M.A. Quliyev ◽  
◽  
U.V. Qurbanova
Keyword(s):  
Inverse Problem ◽  
Unbounded Domain ◽  
Parabolic Equations ◽  
System Of Parabolic Equations ◽  
Multidimensional Inverse Problem

scholarly journals On the recovery of the doping profile in an time-dependent drift-diffusion model

2014 ◽  
Vol 22 (2) ◽  
pp. 253-274
Author(s):  
Bin Wu ◽  
Zewen Wang
Keyword(s):  
Inverse Problem ◽  
Diffusion Model ◽  
Electric Potential ◽  
Parabolic Equations ◽  
Time Dependent ◽  
Doping Profile ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
System Of Parabolic Equations ◽  
Theoretical Results

AbstractWe consider an inverse problem arising from an time-dependent drift-diffusion model in semiconductor devices, which is formulated in terms of a system of parabolic equations for the electron and hole densities and the Poisson equation for the electric potential. This inverse problem aims to identify the doping profile from the final overdetermination data of the electric potential. By using the Schauder’s fixed point theorem in suitable Sobolev space, the existence of this inverse problem are obtained. Moreover by means of Gronwall inequality, we prove the uniqueness of this inverse problem for small measurement time. For this nonlinear inverse problem, our theoretical results guarantee the solvability for the proposed physical model.

An inverse problem for a system of parabolic equations

2007 ◽  
Vol 43 (3) ◽  
pp. 371-380
Author(s):  
A. M. Kadiyev ◽  
V. I. Maksimov
Keyword(s):  
Inverse Problem ◽  
Parabolic Equations ◽  
System Of Parabolic Equations

scholarly journals An inverse problem of radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
El Mustapha Ait Ben Hassi ◽  
Salah-Eddine Chorfi ◽  
Lahcen Maniar
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Stability Result ◽  
Stability Estimate ◽  
Lipschitz Stability ◽  
Dynamic Boundary Conditions ◽  
Logarithmic Convexity ◽  
Dynamic Boundary ◽  
Logarithmic Stability

Abstract We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability estimate for the relevant potentials using a recent Carleman estimate, and a logarithmic stability result for the initial temperatures by a logarithmic convexity method, based on observations in an arbitrary subdomain.

scholarly journals Multidimensional computational models of gas combustion in heterogeneous porous medium

2021 ◽  
Vol 2099 (1) ◽  
pp. 012010
Author(s):  
Yu Laevsky ◽  
T Nosova
Keyword(s):  
Porous Medium ◽  
Parabolic Equations ◽  
Computational Models ◽  
Front Propagation ◽  
Original Model ◽  
Gas Mixture ◽  
Heterogeneous Porous Medium ◽  
Gas Combustion ◽  
Piecewise Constant ◽  
System Of Parabolic Equations

Abstract The processes of filtration gas combustion in heterogeneous porous medium is studying. The presence of two opposite modes of front propagation made it possible to stabilize the combustion front in a composite porous medium with piecewise constant porosity. A feature of this study is the presentation of the original model not in the traditional form of a system of parabolic equations, but in the form of integral conservation laws in terms of the temperature of the porous medium, the total gas enthalpy, and the mass of gas mixture, and the fluxes corresponding to these functions.

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