scholarly journals Lipschitz stability estimate in the inverse Robin problem for the Stokes system

2013 ◽  
Vol 351 (13-14) ◽  
pp. 527-531
Author(s):  
Anne-Claire Egloffe
Keyword(s):  
Stokes System ◽  
Stability Estimate ◽  
Robin Problem ◽  
Lipschitz Stability

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.

ON THE ROBIN PROBLEM FOR STOKES AND NAVIER–STOKES SYSTEMS

2006 ◽  
Vol 16 (05) ◽  
pp. 701-716 ◽  
Author(s):  
REMIGIO RUSSO ◽  
ALFONSINA TARTAGLIONE
Keyword(s):  
Boundary Layer ◽  
Weak Solution ◽  
Lipschitz Domain ◽  
Stokes System ◽  
Navier Stokes ◽  
Robin Problem ◽  
Layer Potentials ◽  
Very Weak Solution ◽  
Stokes Systems ◽  
Compact Boundary

The Robin problem for Stokes and Navier–Stokes systems is considered in a Lipschitz domain with a compact boundary. By making use of the boundary layer potentials approach, it is proved that for Stokes system this problem admits a very weak solution under suitable assumptions on the boundary datum. A similar result is proved for the Navier–Stokes system, provided that the datum is "sufficiently small".

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 On the travel time tomography problem in 3D

2019 ◽  
Vol 27 (4) ◽  
pp. 591-607 ◽  
Author(s):  
Michael V. Klibanov
Keyword(s):  
Fourier Series ◽  
Travel Time ◽  
Orthonormal Basis ◽  
Stability Estimate ◽  
Trigonometric Fourier Series ◽  
Lipschitz Stability ◽  
Spatial Variables ◽  
Travel Time Tomography ◽  
Globally Convergent ◽  
Truncated Fourier Series

Abstract Numerical issues for the 3D travel time tomography problem with non-overdetemined data are considered. Truncated Fourier series with respect to a special orthonormal basis of functions depending on the source position is used. In addition, truncated trigonometric Fourier series with respect to two out of three spatial variables are used. First, the Lipschitz stability estimate is obtained. Next, a globally convergent numerical method is constructed using a Carleman estimate for an integral operator.

Inverse source problem for a generalized Korteweg–de Vries equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Anbu Arivazhagan ◽  
Kumarasamy Sakthivel ◽  
Natesan Barani Balan
Keyword(s):  
Source Term ◽  
Regularity Result ◽  
Stability Estimate ◽  
Lipschitz Stability ◽  
De Vries ◽  
Seventh Order ◽  
Neumann Type ◽  
Type Boundary ◽  
Boundary Stability ◽  
Stability Results

AbstractIn this paper, we consider a seventh-order generalized Korteweg–de Vries (GKdV) equation and study the boundary stability results concerning the inverse problem of recovering a space-dependent source term. We establish a new boundary Carleman estimate for the seventh-order linear operator with the Dirichlet–Neumann type boundary conditions. Using this crucial estimate along with regularity result of the nonlinear GKdV equation, we establish a Lipschitz stability estimate of GKdV equation.

scholarly journals A Lipschitz Stability Estimate for the Inverse Source Problem and the Numerical Scheme

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Xianzheng Jia
Keyword(s):  
Heat Equation ◽  
Numerical Algorithm ◽  
Numerical Scheme ◽  
Source Term ◽  
Stability Estimate ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Inverse Source Problem ◽  
Lipschitz Stability ◽  
Piecewise Constant

We consider the inverse source problem for heat equation, where the source term has the formf(t)ϕ(x). We give a numerical algorithm to compute unknown source termf(t). Also, we give a stability estimate in the case thatf(t)is a piecewise constant function.

scholarly journals Simultaneous determination of the magnetic field and the electric potential in the Schrödinger equation by a finite number of boundary observations

2018 ◽  
Vol 26 (2) ◽  
pp. 201-209 ◽  
Author(s):  
Ibtissem Ben Aïcha ◽  
Youssef Mejri
Keyword(s):  
Magnetic Field ◽  
Schrödinger Equation ◽  
Finite Number ◽  
Electric Potential ◽  
Schrodinger Equation ◽  
Initial Conditions ◽  
Stability Estimate ◽  
Lipschitz Stability ◽  
The Magnetic Field

AbstractWe study the inverse problem of determining the magnetic field and the electric potential appearing in the magnetic Schrödinger equation from the knowledge of a finite number of lateral observations of the solution. We prove a Lipschitz stability estimate for both coefficients simultaneously by choosing the “initial” conditions suitably.

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