Stability and asymptotic behaviour of one-dimensional solutions in cylinders
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917099429953536 |
|---|---|
| author | De Marchis, Francesca Mazzuoli, Lisa Pacella, Filomena |
| author_facet | De Marchis, Francesca Mazzuoli, Lisa Pacella, Filomena |
| contents | We consider positive one-dimensional solutions of a Lane-Emden relative Dirichlet problem in a cylinder and study their stability/instability properties as the energy varies with respect to domain perturbations. This depends on the exponent $p >1$ of the nonlinearity and we obtain results for $p$ close to 1 and for $p$ large. This is achieved by a careful asymptotic analysis of the one-dimensional solution as $p \to 1$ or $p \to \infty$, which is of independent interest. It allows to detect the limit profile and other qualitative properties of these solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09648 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability and asymptotic behaviour of one-dimensional solutions in cylinders De Marchis, Francesca Mazzuoli, Lisa Pacella, Filomena Analysis of PDEs We consider positive one-dimensional solutions of a Lane-Emden relative Dirichlet problem in a cylinder and study their stability/instability properties as the energy varies with respect to domain perturbations. This depends on the exponent $p >1$ of the nonlinearity and we obtain results for $p$ close to 1 and for $p$ large. This is achieved by a careful asymptotic analysis of the one-dimensional solution as $p \to 1$ or $p \to \infty$, which is of independent interest. It allows to detect the limit profile and other qualitative properties of these solutions. |
| title | Stability and asymptotic behaviour of one-dimensional solutions in cylinders |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.09648 |