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Remarks on the theory of elasticity

Sergio Conti, Camillo de Lellis (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In compressible Neohookean elasticity one minimizes functionals which are composed by the sum of the L 2 norm of the deformation gradient and a nonlinear function of the determinant of the gradient. Non–interpenetrability of matter is then represented by additional invertibility conditions. An existence theory which includes a precise notion of invertibility and allows for cavitation was formulated by Müller and Spector in 1995. It applies, however, only if some L p -norm of the gradient with p > 2 is controlled...

Remarks on weak stabilization of semilinear wave equations

Alain Haraux (2001)

ESAIM: Control, Optimisation and Calculus of Variations

If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble....

Remarks on weak stabilization of semilinear wave equations

Alain Haraux (2010)

ESAIM: Control, Optimisation and Calculus of Variations

If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble. ...

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