scholarly journals Operators of order 2\begin{document}$ n $\end{document} with interior degeneracy

2018 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Genni Fragnelli ◽  
◽  
Jerome A. Goldstein ◽  
Rosa Maria Mininni ◽  
Silvia Romanelli ◽  
...  
Keyword(s):  
Interior Degeneracy

scholarly journals An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Khalid Atifi ◽  
Idriss Boutaayamou ◽  
Hamed Ould Sidi ◽  
Jawad Salhi
Keyword(s):  
Numerical Solution ◽  
Parabolic Equations ◽  
Measurement Data ◽  
Gradient Methods ◽  
Stability Estimate ◽  
Inverse Source Problem ◽  
Output Least Squares ◽  
Singular Parabolic Equations ◽  
Interior Degeneracy ◽  
Least Squares Approach

The main purpose of this work is to study an inverse source problem for degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain. Using Carleman estimates, we prove a Lipschitz stability estimate for the source term provided that additional measurement data are given on a suitable interior subdomain. For the numerical solution, the reconstruction is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. The Fréchet differentiability of the Tikhonov functional and the Lipschitz continuity of the Fréchet gradient are proved. These properties allow us to apply gradient methods for numerical solution of the considered inverse source problem.

scholarly journals Carleman estimates for singular parabolic equations with interior degeneracy and non-smooth coefficients

2017 ◽  
Vol 6 (1) ◽  
pp. 61-84 ◽  
Author(s):  
Genni Fragnelli ◽  
Dimitri Mugnai
Keyword(s):  
Parabolic Equations ◽  
Spatial Domain ◽  
Carleman Estimates ◽  
Dirichlet Problems ◽  
Smooth Coefficients ◽  
Degenerate Parabolic ◽  
Singular Parabolic Equations ◽  
Interior Degeneracy

AbstractWe establish Carleman estimates for singular/degenerate parabolic Dirichlet problems with degeneracy and singularity occurring in the interior of the spatial domain. Our results are completely new, since this situation is not covered by previous contributions for degeneracy and singularity on the boundary. In addition, we consider non-smooth coefficients, thus preventing the use of standard calculations in this framework.

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.

Null Controllability for Parabolic Operators with Interior Degeneracy and One-Sided Control

2019 ◽  
Vol 57 (2) ◽  
pp. 900-924
Author(s):  
Piermarco Cannarsa ◽  
Roberto Ferretti ◽  
Patrick Martinez
Keyword(s):  
Null Controllability ◽  
Interior Degeneracy
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