Generic well-posedness of a linear inverse parabolic problem with diffusion parameters

1999 ◽  
Vol 7 (3) ◽  
Author(s):  
M. CHOULLI ◽  
M. YAMAMOTO
Keyword(s):  
Parabolic Problem ◽  
Well Posedness ◽  
Diffusion Parameters ◽  
Inverse Parabolic Problem

Inverse problems for parabolic equations with interior degeneracy and Neumann boundary conditions

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Idriss Boutaayamou ◽  
Genni Fragnelli ◽  
Lahcen Maniar
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Parabolic Problem ◽  
Neumann Boundary ◽  
Spatial Domain ◽  
Neumann Boundary Conditions ◽  
Well Posedness ◽  
Degeneracy Point ◽  
Inverse Source Problems ◽  
Interior Degeneracy

AbstractWe consider a parabolic problem with degeneracy in the interior of the spatial domain and we focus on the well-posedness of the problem and on inverse source problems. The novelties of the present paper are two. First, the degeneracy point is in the interior of the spatial domain. Second, we consider Neumann boundary conditions so that no previous result can be adapted to this situation.

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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