L-p - L-q estimates for a parameter-dependent multiplier with oscillatory and diffusive components

Autor(es)

D'Abbicco, Marcello ^[1] ; Ebert, Marcelo Rempel ^[2]

Afiliação do(s) autor(es)

^[1] Univ Bari, Dept Math, Via E Orabona 4, I-70125 Bari - Italy

^[2] Univ Sao Paulo, Dept Comp & Matemat, BR-14040901 Ribeirao Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 504, n. 1 DEC 1 2021.
• Citações Web of Science: 0

Resumo

In this paper, we derive long time L-p - L-q decay estimates, in the full range 1 <= p <= q <= infinity, for time-dependent multipliers in which an interplay between an oscillatory component and a diffusive component with different scaling appears. We estimate parallel to m(t, .)parallel to M-p(q) as t -> infinity for multipliers of type m(t, xi) = e(+/- i vertical bar xi vertical bar sigma t-vertical bar xi vertical bar theta t), and suitable perturbations, under the assumption that the scaling of the diffusive component is worse, i.e., theta > sigma. These multipliers are, for instance, related to the fundamental solution to the Cauchy problem for the sigma-evolution equation with structural damping: u(tt) + (-Delta)(sigma)u + (-Delta)(theta/2) u(t) = 0, t >= 0, x is an element of R-n, in the so-called non-effective case sigma < theta. (C) 2021 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 20/08276-9 - Método da fase estacionária e aplicações para equações diferenciais parciais de evolução
• Beneficiário: Marcelo Rempel Ebert
• Modalidade de apoio: Auxílio à Pesquisa - Regular