scholarly journals On a class of degenerate parabolic equations with dynamic boundary conditions

2012 ◽  
Vol 253 (1) ◽  
pp. 126-166 ◽  
Author(s):  
Ciprian G. Gal
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary ◽  
Degenerate Parabolic

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.

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