In this note, we prove the global existence of small data solutions for a semilinear wave equation with structural damping, utt - Δu + μ(-Δ)1/2 ut = |u|p, for any n ≥ 2 and p > 1 + 2/(n - 1). The damping term allows us to derive linear Lq1 - Lq2 estimates, for 1 ≤ q1 ≤ q2 ≤ ∞, without loss of regularity, in any space dimension. These estimates provide the basic tool to state our result, in which we assume initial data to be small in (L1 ∩ H1 ∩ L∞)×(L1 ∩ Ln).
A benefit from the L∞ smallness of initial data for the semilinear wave equation with structural damping
D'ABBICCO, MARCELLO
2015-01-01
Abstract
In this note, we prove the global existence of small data solutions for a semilinear wave equation with structural damping, utt - Δu + μ(-Δ)1/2 ut = |u|p, for any n ≥ 2 and p > 1 + 2/(n - 1). The damping term allows us to derive linear Lq1 - Lq2 estimates, for 1 ≤ q1 ≤ q2 ≤ ∞, without loss of regularity, in any space dimension. These estimates provide the basic tool to state our result, in which we assume initial data to be small in (L1 ∩ H1 ∩ L∞)×(L1 ∩ Ln).File in questo prodotto:
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