Well-posedness and stability results for a swelling porous-heat system of second sound

2021 ◽  
pp. 1-14
Author(s):  
Ahmed Keddi ◽  
Salim A. Messaoudi ◽  
Mohamed Alahyane
Keyword(s):  
Well Posedness ◽  
Second Sound ◽  
Heat System ◽  
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.

General decay in a Timoshenko-type system with thermoelasticity with second sound

2015 ◽  
Vol 4 (4) ◽  
pp. 263-284 ◽  
Author(s):  
Mohamed Ali Ayadi ◽  
Ahmed Bchatnia ◽  
Makram Hamouda ◽  
Salim Messaoudi
Keyword(s):  
Group Theory ◽  
Type System ◽  
General Decay ◽  
Regularity Of Solutions ◽  
Well Posedness ◽  
Second Sound ◽  
Semi Group ◽  
Stability Number ◽  
Timoshenko System ◽  
Relaxation Functions

AbstractIn this article, we consider a vibrating nonlinear Timoshenko system with thermoelasticity with second sound. We discuss the well-posedness and the regularity of solutions using the semi-group theory. Moreover, we establish an explicit and general decay result for a wide class of relaxation functions, which depend on a stability number μ.

A stability result of a Timoshenko system in thermoelasticity of second sound with a delay term in the internal feedback

2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Djamel Ouchenane
Keyword(s):  
Heat Conduction ◽  
Stability Result ◽  
Well Posedness ◽  
Second Sound ◽  
Timoshenko System ◽  
Wave Speeds ◽  
One Dimensional ◽  
Delay Term ◽  
Semigroup Method ◽  
Cattaneo’S Law

AbstractIn this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay term in the feedback. The heat conduction is given by Cattaneo's law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem. Furthermore, an exponential stability result is shown without the usual assumption on the wave speeds. To achieve our goals, we make use of the semigroup method and the energy method.

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