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.

Asymptotic expansion of solutions to an inverse problem of parabolic type with non-homogeneous boundary conditions

2011 ◽  
Vol 141 (4) ◽  
pp. 777-817 ◽  
Author(s):  
Davide Guidetti
Keyword(s):  
Inverse Problem ◽  
Asymptotic Expansion ◽  
Boundary Conditions ◽  
General Result ◽  
Parabolic Problem ◽  
Source Function ◽  
Parabolic Type ◽  
Time Dependent ◽  
Asymptotic Expansion Of Solutions ◽  
Inverse Parabolic Problem

We consider an inverse parabolic problem of reconstruction of the source function, together with the traditional solution. In contrast with older literature, we consider non-homogeneous and time-dependent boundary conditions. We are able to prove a general result of convergence to a stationary state, and of asymptotic expansion as t → ∞.

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