scholarly journals Well-posedness and stability results for the Gardner equation

2011 ◽  
Vol 19 (4) ◽  
pp. 503-520 ◽  
Author(s):  
Miguel A. Alejo
Keyword(s):  
Well Posedness ◽  
Gardner Equation ◽  
Stability Results

scholarly journals A Convex Variational Model for Learning Convolutional Image Atoms from Incomplete Data

2019 ◽  
Vol 62 (3) ◽  
pp. 417-444
Author(s):  
A. Chambolle ◽  
M. Holler ◽  
T. Pock
Keyword(s):  
Image Reconstruction ◽  
Inverse Problems ◽  
Incomplete Data ◽  
Variational Model ◽  
Well Posedness ◽  
Optimal Solutions ◽  
Analytical Properties ◽  
Numerical Performance ◽  
Stability Results ◽  
Continuous Setting

AbstractA variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is convex and allows for simultaneous image reconstruction and atom learning in a general, inverse problems context. Further, motivated by an improved numerical performance, also a semi-convex variant is included in the analysis and the experiments of the paper. For both settings, fundamental analytical properties allowing in particular to ensure well-posedness and stability results for inverse problems are proven in a continuous setting. Exploiting convexity, globally optimal solutions are further computed numerically for applications with incomplete, noisy and blurry data and numerical results are shown.

Unilateral problems for the wave equation with degenerate and localized nonlinear damping: well-posedness and non-stability results

2018 ◽  
Vol 291 (8-9) ◽  
pp. 1216-1239
Author(s):  
A. D. D. Cavalcanti ◽  
M. M. Cavalcanti ◽  
L. H. Fatori ◽  
M. A. Jorge Silva
Keyword(s):  
Wave Equation ◽  
Nonlinear Damping ◽  
Well Posedness ◽  
Unilateral Problems ◽  
Stability Results
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