| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [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
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 504, n. 1 DEC 1 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 20/08276-9 - The stationary phase method and applications to evolution partial differential equations |
| Grantee: | Marcelo Rempel Ebert |
| Support Opportunities: | Regular Research Grants |