Abstract: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.
| Comments: | 32 pages. An application has been added |
| Subjects: | Functional Analysis (math.FA); Analysis of PDEs (math.AP) |
| MSC classes: | 34G10, 34G20, 35J10, 35L05, 35L90, 47B12 |
| Cite as: | arXiv:2601.19075 [math.FA] |
| (or arXiv:2601.19075v2 [math.FA] for this version) | |
| https://doi.org/10.48550/arXiv.2601.19075 arXiv-issued DOI via DataCite |
From: Nikolaos Roidos Prof. Dr. [view email]
[v1]
Tue, 27 Jan 2026 01:25:40 UTC (23 KB)
[v2]
Fri, 22 May 2026 08:58:42 UTC (24 KB)
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