The Kawahara equation on star graphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911266313863168 |
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| author | Cavalcante, Márcio Kwak, Chulkwang Marques, José |
| author_facet | Cavalcante, Márcio Kwak, Chulkwang Marques, José |
| contents | In this paper, we establish local well-posedness for the Cauchy problem associated with the Kawahara equation on a general metric star graph. Initially, we identify suitable boundary conditions that produce a well-behaved dynamics for the linear equation. Subsequently, we derive the integral formula using the forcing operator method, previously applied to the Kawahara equation on the half-line by Cavalcante and Kwak (NoDEA 2020), and the Fourier restriction method of Bourgain (GAFA 1993). This work has the potential to be extended to other fifth-order nonlinear dispersive equations on star graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Kawahara equation on star graphs Cavalcante, Márcio Kwak, Chulkwang Marques, José Analysis of PDEs 35Q53, 35R02, 76B15 In this paper, we establish local well-posedness for the Cauchy problem associated with the Kawahara equation on a general metric star graph. Initially, we identify suitable boundary conditions that produce a well-behaved dynamics for the linear equation. Subsequently, we derive the integral formula using the forcing operator method, previously applied to the Kawahara equation on the half-line by Cavalcante and Kwak (NoDEA 2020), and the Fourier restriction method of Bourgain (GAFA 1993). This work has the potential to be extended to other fifth-order nonlinear dispersive equations on star graphs. |
| title | The Kawahara equation on star graphs |
| topic | Analysis of PDEs 35Q53, 35R02, 76B15 |
| url | https://arxiv.org/abs/2511.06007 |