Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Roidos, Nikolaos
Institution: University of Patras
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
OpenAlex ID: W7125949346
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