scholarly journals Globally strictly convex cost functional for an inverse parabolic problem

2015 ◽  
Vol 39 (4) ◽  
pp. 930-940 ◽  
Author(s):  
Michael V. Klibanov ◽  
Vladimir G. Kamburg
Keyword(s):  
Parabolic Problem ◽  
Cost Functional ◽  
Strictly Convex ◽  
Convex Cost ◽  
Inverse Parabolic Problem

scholarly journals Globally Strictly Convex Cost Functional for a 1-D Inverse Medium Scattering Problem with Experimental Data

2017 ◽  
Vol 77 (5) ◽  
pp. 1733-1755 ◽  
Author(s):  
Michael V. Klibanov ◽  
Aleksandr E. Kolesov ◽  
Lam Nguyen ◽  
Anders Sullivan
Keyword(s):  
Experimental Data ◽  
Scattering Problem ◽  
Cost Functional ◽  
Strictly Convex ◽  
Convex Cost ◽  
Inverse Medium ◽  
Inverse Medium Scattering

Stability analysis of an inverse parabolic problem with discontinuous variable coefficient

2011 ◽  
Vol 141 (5) ◽  
pp. 975-999 ◽  
Author(s):  
M. Di Cristo ◽  
S. Vessella
Keyword(s):  
Continuous Dependence ◽  
Variable Coefficient ◽  
Parabolic Problem ◽  
A Priori ◽  
Time Varying ◽  
Variable Function ◽  
Thermal Measurements ◽  
Logarithmic Type ◽  
Anomalous Region ◽  
Inverse Parabolic Problem

We consider a time-varying inclusion in a thermal conductor specimen. In particular, the thermal conductivity is a variable function depending on space and time with a jump of discontinuity along the interface of the unknown anomalous region. Provided with some a priori information on the conductivity and its support, we study the continuous dependence of the inclusion from infinitely many thermal measurements taken on an open portion of the boundary of our specimen. We prove a rate of continuity of logarithmic type showing, in addition, its optimality.

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