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The goal of this paper is to work out a thermodynamical setting for nonisothermal phase-field models with conserved and nonconserved order parameters in thermoelastic materials. Our approach consists in exploiting the second law of thermodynamics in the form of the entropy principle according to I. Müller and I. S. Liu, which leads to the evaluation of the entropy inequality with multipliers.
As the main result we obtain a general scheme of phase-field models which involves an...
This paper studies the exact controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D wave system with a boundary control at one extreme. It is known that usual schemes obtained with finite difference or finite element methods are not uniformly controllable with respect to the discretization parameters and . We introduce an implicit finite difference scheme which differs from the usual centered one by additional terms of order and . Using a discrete...
This paper studies the
exact controllability of a finite dimensional system obtained by
discretizing in space and time the linear 1-D wave system with a
boundary control at one extreme. It is known that usual schemes
obtained with finite difference or finite element methods are not
uniformly controllable with respect to the discretization
parameters h and Δt. We introduce an implicit finite
difference scheme which differs from the usual centered one by
additional terms of order h2 and Δt2. Using...
Here, we prove the uniform observability of a two-grid method for the semi-discretization of the -wave equation for a time ; this time, if the observation is made in , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I 338 (2004) 413–418]. Our proof follows an Ingham type approach.
Here, we prove the uniform observability of a two-grid method
for the semi-discretization of the 1D-wave equation for a time ;
this time, if the observation is made in , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I338 (2004) 413–418].
Our proof follows an Ingham type approach.
We analyze the controllability of the wave equation on a cylinder when the control acts on the
boundary, that does not satisfy the classical geometric control condition.
We obtain precise estimates on the analyticity of reachable functions.
As the control time increases, the degree of analyticity that is required for a function to
be reachable decreases as an inverse power of time.
We conclude that any analytic function can be reached if that control time is large enough.
In the C∞ class, a...
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332