In this paper, we derive L-1-L-1 long time estimates for the strongly damped plate equationu(tt) Delta(2)u Delta(2)u(t) = 0 x is an element of R-n, x is an element of R-n u(0, x) = uo(x), ut(0,x) = uj(x).In particular, we prove thatparallel to u(t, .)parallel to(L-1 <= C(1+t) n/7)parallel to u(0) parallel to L-1 + (1+t)1/2 parallel to u(1)parallel to L-1),for any t > 0, in space dimension n >= 5. (C) 2019 Elsevier Inc. All rights reserved.
L1 − L1 estimates for the strongly damped plate equation
D'Abbicco M.;Girardi G.;
2019-01-01
Abstract
In this paper, we derive L-1-L-1 long time estimates for the strongly damped plate equationu(tt) Delta(2)u Delta(2)u(t) = 0 x is an element of R-n, x is an element of R-n u(0, x) = uo(x), ut(0,x) = uj(x).In particular, we prove thatparallel to u(t, .)parallel to(L-1 <= C(1+t) n/7)parallel to u(0) parallel to L-1 + (1+t)1/2 parallel to u(1)parallel to L-1),for any t > 0, in space dimension n >= 5. (C) 2019 Elsevier Inc. All rights reserved.File in questo prodotto:
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