Spectral gap global solutions for degenerate Kirchhoff equations
| dc.creator | Ghisi, Marina | |
| dc.creator | Gobbino, Massimo | |
| dc.date | 2008-07-28 | |
| dc.date.accessioned | 2026-07-07T09:53:16Z | |
| dc.date.available | 2026-07-07T09:53:16Z | |
| dc.description | We consider the second order Cauchy problem $$u''+m(|A^{1/2}u|^2)Au=0, u(0)=u_{0}, u'(0)=u_{1},$$ where $m:[0,+\infty)\to[0,+\infty)$ is a continuous function, and $A$ is a self-adjoint nonnegative operator with dense domain on a Hilbert space. It is well known that this problem admits local-in-time solutions provided that $u_{0}$ and $u_{1}$ are regular enough, depending on the continuity modulus of $m$, and on the strict/weak hyperbolicity of the equation. We prove that for such initial data $(u_{0},u_{1})$ there exist two pairs of initial data $(\overline{u}_{0},\overline{u}_{1})$, $(\widehat{u}_{0},\widehat{u}_{1})$ for which the solution is global, and such that $u_{0}=\overline{u}_{0}+\widehat{u}_{0}$, $u_{1}=\overline{u}_{1}+\widehat{u}_{1}$. This is a byproduct of a global existence result for initial data with a suitable spectral gap, which extends previous results obtained in the strictly hyperbolic case with a smooth nonlinearity $m$. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/0807.4381 | |
| dc.identifier | http://arxiv.org/abs/0807.4381 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165889 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L70, 35L80, 35L90 | |
| dc.title | Spectral gap global solutions for degenerate Kirchhoff equations | |
| dc.type | text |