Self-similar Differential Equations
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910605175160832 |
|---|---|
| author | Brin, Leon Q. Fields, Joe |
| author_facet | Brin, Leon Q. Fields, Joe |
| contents | Differential equations where the graph of some derivative of a function is composed of a finite number of similarity transformations of the graph of the function itself are defined. We call these self-similar differential equations (SSDEs) and prove existence and uniqueness of solution under certain conditions. While SSDEs are not ordinary differential equations, the technique for demonstrating existence and uniqueness of SSDEs parallels that for ODEs. This paper appears to be the first work on equations of this nature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09943 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-similar Differential Equations Brin, Leon Q. Fields, Joe Classical Analysis and ODEs 34A99 Differential equations where the graph of some derivative of a function is composed of a finite number of similarity transformations of the graph of the function itself are defined. We call these self-similar differential equations (SSDEs) and prove existence and uniqueness of solution under certain conditions. While SSDEs are not ordinary differential equations, the technique for demonstrating existence and uniqueness of SSDEs parallels that for ODEs. This paper appears to be the first work on equations of this nature. |
| title | Self-similar Differential Equations |
| topic | Classical Analysis and ODEs 34A99 |
| url | https://arxiv.org/abs/2409.09943 |