We consider a second order linear evolution equation with a dissipative term multiplied by a time-dependent coefficient. Our aim is to design the coefficient in such a way that all solutions decay in time as fast as possible. We discover that constant coefficients do not achieve the goal and neither do time-dependent coefficients, if they are uniformly too big. On the contrary, pulsating coefficients which alternate big and small values in a suitable way prove to be more effective. Our theory applies to ordinary differential equations, systems of ordinary differential equations, and partial differential equations of hyperbolic type.

The remarkable effectiveness of time-dependent damping terms for second order evolution equations

GHISI, MARINA;GOBBINO, MASSIMO;
2016

Abstract

We consider a second order linear evolution equation with a dissipative term multiplied by a time-dependent coefficient. Our aim is to design the coefficient in such a way that all solutions decay in time as fast as possible. We discover that constant coefficients do not achieve the goal and neither do time-dependent coefficients, if they are uniformly too big. On the contrary, pulsating coefficients which alternate big and small values in a suitable way prove to be more effective. Our theory applies to ordinary differential equations, systems of ordinary differential equations, and partial differential equations of hyperbolic type.
Ghisi, Marina; Gobbino, Massimo; Haraux, Alain
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/809459
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