We consider the Cauchy problem for the semi-linear damped wave equation utt -Δu + b(t)ut = f (t, u), u(0, x) = uo (x), ut(0,x) = u1 (x). We prove the global existence of small data solution in low space dimension, and we derive (Lm∩ L2) - L2 decay estimates, for m ∈ [1, 2). We assume that the time-dependent damping term b(t) > 0 is effective, that is, the equation inherits some properties of the parabolic equation b(t)ut - Δu = f (t, u).
Small data solutions for semilinear wave equations with effective damping
D'ABBICCO, MARCELLO
2013-01-01
Abstract
We consider the Cauchy problem for the semi-linear damped wave equation utt -Δu + b(t)ut = f (t, u), u(0, x) = uo (x), ut(0,x) = u1 (x). We prove the global existence of small data solution in low space dimension, and we derive (Lm∩ L2) - L2 decay estimates, for m ∈ [1, 2). We assume that the time-dependent damping term b(t) > 0 is effective, that is, the equation inherits some properties of the parabolic equation b(t)ut - Δu = f (t, u).File in questo prodotto:
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