Finding the exact decay rate of all solutions to some second order evolution equations with dissipationReportar como inadecuado




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1 dm.unipi - Dipartimento di Matematica 2 dm.unipi - Dipartimento di Matematica 3 LJLL - Laboratoire Jacques-Louis Lions

Abstract : We consider an abstract second order evolution equation with damping. The ``elastic- term is represented by a self-adjointnonnegative operator $A$ with discrete spectrum, and the nonlinear term has order greater than one at the origin. We investigate the asymptotic behavior of solutions.We prove the coexistence of slow solutions and fast solutions. Slow solutions live close to the kernel of $A$, and decay asnegative powers of $t$ as solutions of the first order equation obtained by neglecting the operator $A$ and the second ordertime-derivatives in the original equation. Fast solutions live close to the range of $A$ and decay exponentially as solutions ofthe linear homogeneous equation obtained by neglecting the nonlinear terms in the original equation.The abstract results apply to semilinear dissipative hyperbolicequations.





Autor: Marina Ghisi - Massimo Gobbino - Alain Haraux -

Fuente: https://hal.archives-ouvertes.fr/



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