Strip-type operators and abstract Cauchy problems
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913153617494016 |
|---|---|
| author | Roidos, Nikolaos |
| author_facet | Roidos, Nikolaos |
| contents | We consider the non-homogeneous abstract linear Schrödinger and wave equations with zero initial conditions, defined by operators of strip-type and parabola-type in Banach spaces, respectively, and establish the well-posedness of classical solutions in appropriate vector-valued Sobolev-Slobodetskii spaces. We obtain analogous results for two extensions of these equations by replacing the previously mentioned boundedness properties of the associated operators with $R$-boundedness. As an application, we consider an abstract semilinear wave equation and establish the existence and uniqueness of classical solutions to this problem for short times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19075 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strip-type operators and abstract Cauchy problems Roidos, Nikolaos Functional Analysis Analysis of PDEs 34G10, 34G20, 35J10, 35L05, 35L90, 47B12 We consider the non-homogeneous abstract linear Schrödinger and wave equations with zero initial conditions, defined by operators of strip-type and parabola-type in Banach spaces, respectively, and establish the well-posedness of classical solutions in appropriate vector-valued Sobolev-Slobodetskii spaces. We obtain analogous results for two extensions of these equations by replacing the previously mentioned boundedness properties of the associated operators with $R$-boundedness. As an application, we consider an abstract semilinear wave equation and establish the existence and uniqueness of classical solutions to this problem for short times. |
| title | Strip-type operators and abstract Cauchy problems |
| topic | Functional Analysis Analysis of PDEs 34G10, 34G20, 35J10, 35L05, 35L90, 47B12 |
| url | https://arxiv.org/abs/2601.19075 |