Hölder Stability in Linear Anisotropic Viscoelasticity

1975 ◽  
pp. 190-195
Author(s):  
C. E. Beevers
Keyword(s):  
Hölder Stability

Estimation of the Time-Dependent Body Force Needed to Exert on a Membrane to Reach a Desired State at the Final Time

2019 ◽  
Vol 19 (2) ◽  
pp. 323-339
Author(s):  
Lyubomir Boyadjiev ◽  
Kamal Rashedi ◽  
Mourad Sini
Keyword(s):  
Body Force ◽  
Single Point ◽  
Finite Size ◽  
Numerical Procedure ◽  
Time Dependent ◽  
Final Time ◽  
Initial Shape ◽  
Additional Information ◽  
Boundary Force ◽  
Hölder Stability

AbstractWe are concerned with the wave propagation in a homogeneous 2D or 3D membrane Ω of finite size. We assume that either the membrane is initially at rest or we know its initial shape (but not necessarily both) and its boundary is subject to a known boundary force. We address the question of estimating the needed time-dependent body force to exert on the membrane to reach a desired state at a given final time T. As an additional information, we ask for the displacement on the boundary. We consider the displacement either at a single point of the boundary or on the whole boundary. First, we show the uniqueness of solution of these inverse problems under natural conditions on the final time T. If, in addition, the displacement on the whole boundary is only time dependent (which means that the boundary moves with a constant speed), this condition on T is removed if Ω satisfies Schiffer’s property. Second, we derive a conditional Hölder stability inequality for estimating such a time-dependent force. Third, we propose a numerical procedure based on the application of the satisfier function along with the standard Fourier expansion of the solution to the problems. Numerical tests are given to illustrate the applicability of the proposed procedure.

Hölder stability estimates for some inverse pointwise source problems

2012 ◽  
Vol 350 (23-24) ◽  
pp. 1031-1035 ◽  
Author(s):  
Abdellatif El Badia ◽  
Ahmad El Hajj
Keyword(s):  
Stability Estimates ◽  
Hölder Stability

Hölder Stability and Logarithmic Convexity

1971 ◽  
pp. 248-255 ◽  
Author(s):  
R. J. Knops ◽  
L. E. Payne
Keyword(s):  
Logarithmic Convexity ◽  
Hölder Stability

Hölder stability for $$C^r$$ C r central translations

2016 ◽  
Vol 286 (1-2) ◽  
pp. 121-139
Author(s):  
Javier Correa ◽  
Enrique R. Pujals
Keyword(s):  
Hölder Stability

scholarly journals Global stability for an inverse problem in soil–structure interaction

2015 ◽  
Vol 471 (2179) ◽  
pp. 20150117 ◽  
Author(s):  
G. Alessandrini ◽  
A. Morassi ◽  
E. Rosset ◽  
S. Vessella
Keyword(s):  
Inverse Problem ◽  
Soil Structure ◽  
Stability Estimate ◽  
Unknown Coefficient ◽  
Thin Elastic Plate ◽  
Concentrated Force ◽  
Reaction Coefficient ◽  
Slab Foundation ◽  
Interior Points ◽  
Hölder Stability

We consider the inverse problem of determining the Winkler subgrade reaction coefficient of a slab foundation modelled as a thin elastic plate clamped at the boundary. The plate is loaded by a concentrated force and its transversal deflection is measured at the interior points. We prove a global Hölder stability estimate under (mild) regularity assumptions on the unknown coefficient.

scholarly journals Hölder stability of diffeomorphisms

2009 ◽  
Vol 24 (2) ◽  
pp. 315-329
Author(s):  
Jinpeng An ◽  
Keyword(s):  
Hölder Stability
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