scholarly journals Stability result for two coefficients in a coupled hyperbolic-parabolic system

2017 ◽  
Vol 25 (3) ◽  
Author(s):  
Patricia Gaitan ◽  
Hadjer Ouzzane
Keyword(s):  
Inverse Problem ◽  
Parabolic System ◽  
Stability Result ◽  
Fixed Time ◽  
Spatial Domain ◽  
Carleman Estimates ◽  
Observation Data ◽  
Lipschitz Stability

AbstractThis work is concerned with the study of the inverse problem of determining two coefficients in a hyperbolic-parabolic system using the following observation data: an interior measurement of only one component and data of two components at a fixed time over the whole spatial domain. A Lipschitz stability result is proved using Carleman estimates.

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.

Lipschitz stability estimates in inverse source problems for a fractional diffusion equation of half order in time by Carleman estimates

2018 ◽  
Vol 26 (5) ◽  
pp. 647-672 ◽  
Author(s):  
Atsushi Kawamoto
Keyword(s):  
Diffusion Equation ◽  
Additional Data ◽  
Fixed Time ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Carleman Estimates ◽  
Time Interval ◽  
Stability Estimates ◽  
Lipschitz Stability ◽  
Inverse Source Problems

Abstract In this article, we consider a fractional diffusion equation of half order in time. We study inverse problems of determining the space-dependent factor in the source term from additional data at a fixed time and interior or boundary data over an appropriate time interval. We establish the global Lipschitz stability estimates in the inverse source problems. Our methods are based on Carleman estimates. Here we prove and use the Carleman estimates for a fractional diffusion equation of half order in time.

scholarly journals Stability estimate for a strongly coupled parabolic system

2012 ◽  
Vol 43 (1) ◽  
pp. 137-144 ◽  
Author(s):  
Kun-Chu Chen
Keyword(s):  
Parabolic System ◽  
Stability Estimate ◽  
Carleman Estimates ◽  
Inverse Source Problem ◽  
Lipschitz Stability ◽  
Strongly Coupled

We consider an inverse source problem for a 2×2 strongly coupled parabolic system. The Lipschitz stability is proved and the proof is based on the Carleman estimates with two large parameters.

scholarly journals Identification of points sources via time fractional diffusion equation

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6189-6201 ◽  
Author(s):  
A. Ghanmi ◽  
R. Mdimagh ◽  
I.B. Saad
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Stability Result ◽  
Fractional Diffusion ◽  
Cauchy Data ◽  
Diffusion Equations ◽  
Lipschitz Stability ◽  
Single Measurement ◽  
Fractional Diffusion Equations ◽  
Time Fractional Diffusion Equation

This article investigates the source identification in the fractional diffusion equations, by performing a single measurement of the Cauchy data on the accessible boundary. The main results of this work consist in giving an identifiability result and establishing a local Lipschitz stability result. To solve the inverse problem of identifying fractional sources from such observations, a non-iterative algebraical method based on the Reciprocity Gap functional is proposed.

scholarly journals Determination of the order of fractional derivative for subdiffusion equations

2020 ◽  
Vol 23 (6) ◽  
pp. 1647-1662
Author(s):  
Ravshan Ashurov ◽  
Sabir Umarov
Keyword(s):  
Fractional Derivative ◽  
Fixed Time ◽  
Time Instant ◽  
Observation Data ◽  
Additional Information ◽  
Fractional Modeling ◽  
Time Fractional Derivative ◽  
The Right ◽  
Right Order

Abstract The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation with an arbitrary second order elliptic differential operator. We prove that the additional information about the solution at a fixed time instant at a monitoring location, as “the observation data”, identifies uniquely the order of the fractional derivative.

Inverse problem for a degenerate/singular parabolic system with Neumann boundary conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammed Alaoui ◽  
Abdelkarim Hajjaj ◽  
Lahcen Maniar ◽  
Jawad Salhi
Keyword(s):  
Boundary Conditions ◽  
Parabolic System ◽  
Source Term ◽  
Neumann Boundary ◽  
Stability Estimate ◽  
Carleman Estimates ◽  
Well Posedness ◽  
Degenerate Diffusion ◽  
Neumann Type ◽  
Lower Order Terms

AbstractIn this paper, we study an inverse source problem for a degenerate and singular parabolic system where the boundary conditions are of Neumann type. We consider a problem with degenerate diffusion coefficients and singular lower-order terms, both vanishing at an interior point of the space domain. In particular, we address the question of well-posedness of the problem, and then we prove a stability estimate of Lipschitz type in determining the source term by data of only one component. Our method is based on Carleman estimates, cut-off procedures and a reflection technique.

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