A two spaces extension of Cauchy-Lipschitz Theorem
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914696728150016 |
|---|---|
| author | Bertucci, Charles Lions, Pierre Louis |
| author_facet | Bertucci, Charles Lions, Pierre Louis |
| contents | We adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary differential equations, we consider $\dot{x} = f(x,x)$ for a function $f: V\times E \to E$ where $E$ is a Banach space and $V \hookrightarrow E$ a normed vector space. This structure allows us to distinguish between the two dependencies of $f$ in $x$ and allows to generalize classical results. We also prove a similar results for partial differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19092 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A two spaces extension of Cauchy-Lipschitz Theorem Bertucci, Charles Lions, Pierre Louis Analysis of PDEs We adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary differential equations, we consider $\dot{x} = f(x,x)$ for a function $f: V\times E \to E$ where $E$ is a Banach space and $V \hookrightarrow E$ a normed vector space. This structure allows us to distinguish between the two dependencies of $f$ in $x$ and allows to generalize classical results. We also prove a similar results for partial differential equations. |
| title | A two spaces extension of Cauchy-Lipschitz Theorem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.19092 |