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Well-posedness and stability for a nonlinear Euler-Bernoulli beam equation
- Source :
- Communications in Analysis and Mechanics, Vol 16, Iss 1, Pp 193-216 (2024)
- Publication Year :
- 2024
- Publisher :
- AIMS Press, 2024.
-
Abstract
- We study the well-posedness and stability for a nonlinear Euler-Bernoulli beam equation modeling railway track deflections in the framework of input-to-state stability (ISS) theory. More specifically, in the presence of both distributed in-domain and boundary disturbances, we prove first the existence and uniqueness of a classical solution by using the technique of lifting and the semigroup method, and then establish the $ L^r $-integral input-to-state stability estimate for the solution whenever $ r\in [2, +\infty] $ by constructing a suitable Lyapunov functional with the aid of Sobolev-like inequalities, which are used to deal with the boundary terms. We provide an extensive extension of relevant work presented in the existing literature.
Details
- Language :
- English
- ISSN :
- 28363310
- Volume :
- 16
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Communications in Analysis and Mechanics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.391580da9ba649b18296e64da7259f03
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/cam.2024009?viewType=HTML