A uniqueness result for Kirchhoff equations with non-Lipschitz nonlinear term
| dc.creator | Ghisi, Marina | |
| dc.creator | Gobbino, Massimo | |
| dc.date | 2008-07-09 | |
| dc.date.accessioned | 2026-07-07T09:49:22Z | |
| dc.date.available | 2026-07-07T09:49:22Z | |
| dc.description | We consider the second order Cauchy problem $$u''+\m{u}Au=0, u(0)=u_{0}, u'(0)=u_{1},$$ 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 $m$. It is also well known that the solution is unique when $m$ is locally Lipschitz continuous. In this paper we prove that if either $<Au_{0},u_{1}>\neq 0$, or $|A^{1/2}u_{1}|^{2}\neq\m{u_{0}}|Au_{0}|^{2}$, then the local solution is unique even if $m$ is not Lipschitz continuous. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0807.1411 | |
| dc.identifier | http://arxiv.org/abs/0807.1411 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164558 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L70, 35L80, 35L90 | |
| dc.title | A uniqueness result for Kirchhoff equations with non-Lipschitz nonlinear term | |
| dc.type | text |