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Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping

Alexander Y. Khapalov (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We show that the set of nonnegative equilibrium-like states, namely, like ( y d , 0 ) of the semilinear vibrating string that can be reached from any non-zero initial state ( y 0 , y 1 ) ∈ H 0 1 ( 0 , 1 ) × L 2 ( 0 , 1 ) , by varying its axial load and the gain of damping, is dense in the “nonnegative” part of the subspace L 2 ( 0 , 1 ) × { 0 } of L 2 ( 0 , 1 ) × H - 1 ( 0 , 1 ) . Our main results deal with nonlinear terms which admit at most the linear growth at infinity in y and satisfy certain restriction on their total impact on (0,∞) with respect to the time-variable.

Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems

Philippe Moireau, Dominique Chapelle (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered....

Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems

Philippe Moireau, Dominique Chapelle (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered....

Regularity and optimal control of quasicoupled and coupled heating processes

Jiří Jarušek (1996)

Applications of Mathematics

Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions...

Regularity in kinetic formulations via averaging lemmas

Pierre-Emmanuel Jabin, Benoît Perthame (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like γ = 3 in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best known regularizing effect in multidimensional scalar conservation laws. The new ingredient here is to use velocity...

Regularity in kinetic formulations via averaging lemmas

Pierre-Emmanuel Jabin, Benoît Perthame (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like γ = 3 in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best known regularizing effect in multidimensional scalar conservation laws. The new ingredient here is to...

Regularity of displacement solutions in Hencky plasticity. II: The main result

Jarosław L. Bojarski (2011)

Applicationes Mathematicae

The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. Here, a non-homogeneous material is considered, where the elastic-plastic properties change discontinuously. In the first part, we have found the extremal relation between the displacement formulation defined on the space of bounded deformation and the stress formulation of the variational problem in Hencky plasticity. In the second part, we prove that the displacement...

Regularity of displacement solutions in Hencky plasticity. I: The extremal relation

Jarosław L. Bojarski (2011)

Applicationes Mathematicae

The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. A non-homogeneous material whose elastic-plastic properties change discontinuously is considered. We find (in an explicit form) the extremal relation between the displacement formulation (defined on the space of bounded deformation) and the stress formulation of the variational problem in Hencky plasticity. This extremal relation is used in the proof of the regularity of displacements. ...

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