Hyperbolic--parabolic singular perturbation for nondegenerate Kirchhoff equations with critical weak dissipation
| dc.creator | Ghisi, Marina | |
| dc.creator | Gobbino, Massimo | |
| dc.date | 2009-01-01 | |
| dc.date.accessioned | 2026-07-07T12:23:45Z | |
| dc.date.available | 2026-07-07T12:23:45Z | |
| dc.description | We consider the hyperbolic-parabolic singular perturbation problem for a nondegenerate quasilinear equation of Kirchhoff type with weak dissipation. This means that the dissipative term is multiplied by a coefficient b(t) which tends to 0 as t tends to +infinity. The case where b(t) behaves like (1+t)^{-p} with p<1 has recently been considered. The result is that the hyperbolic problem has a unique global solution, and the difference between solutions of the hyperbolic problem and the corresponding solutions of the parabolic problem converges to zero both as t tends to +infinity and as epsilon goes to 0. In this paper we show that these results cannot be true for p>1, but they remain true in the critical case p=1. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/0901.0185 | |
| dc.identifier | http://arxiv.org/abs/0901.0185 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214099 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35B25; 35B40; 35L70. | |
| dc.title | Hyperbolic--parabolic singular perturbation for nondegenerate Kirchhoff equations with critical weak dissipation | |
| dc.type | text |