The Euler-Bernoulli equation with distributional coefficients and forces
- Author
- Robin Blommaert, Srdan Lazendic (UGent) and Ljubica Oparnica (UGent)
- Organization
- Project
- Abstract
- In this work we investigate a very weak solution to the initial-boundary value problem of an Euler-Bernoulli beam model. We allow for bending stiffness, axial-and transversal forces as well as for initial conditions to be irregular functions or distributions. We prove the well-posedness of this problem in the very weak sense. More precisely, we define the very weak solution to the problem and show its existence and uniqueness. For regular enough coefficients we show consistency with the weak solution. Numerical analysis shows that the very weak solution coincides with the weak solution, when the latter exists, but also offers more insights into the behaviour of the very weak solution, when the weak solution doesn’t exist.
- Keywords
- Differential equations with discontinuous coefficients, Very weak solutions to partial differential equations, Functional analytic methods, Energy estimates, WAVE-EQUATION, GENERALIZED SOLUTIONS, WEAK SOLUTIONS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8763887
- MLA
- Blommaert, Robin, et al. “The Euler-Bernoulli Equation with Distributional Coefficients and Forces.” COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol. 123, 2022, pp. 171–83, doi:10.1016/j.camwa.2022.08.011.
- APA
- Blommaert, R., Lazendic, S., & Oparnica, L. (2022). The Euler-Bernoulli equation with distributional coefficients and forces. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 123, 171–183. https://doi.org/10.1016/j.camwa.2022.08.011
- Chicago author-date
- Blommaert, Robin, Srdan Lazendic, and Ljubica Oparnica. 2022. “The Euler-Bernoulli Equation with Distributional Coefficients and Forces.” COMPUTERS & MATHEMATICS WITH APPLICATIONS 123: 171–83. https://doi.org/10.1016/j.camwa.2022.08.011.
- Chicago author-date (all authors)
- Blommaert, Robin, Srdan Lazendic, and Ljubica Oparnica. 2022. “The Euler-Bernoulli Equation with Distributional Coefficients and Forces.” COMPUTERS & MATHEMATICS WITH APPLICATIONS 123: 171–183. doi:10.1016/j.camwa.2022.08.011.
- Vancouver
- 1.Blommaert R, Lazendic S, Oparnica L. The Euler-Bernoulli equation with distributional coefficients and forces. COMPUTERS & MATHEMATICS WITH APPLICATIONS. 2022;123:171–83.
- IEEE
- [1]R. Blommaert, S. Lazendic, and L. Oparnica, “The Euler-Bernoulli equation with distributional coefficients and forces,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol. 123, pp. 171–183, 2022.
@article{8763887,
abstract = {{In this work we investigate a very weak solution to the initial-boundary value problem of an Euler-Bernoulli beam model. We allow for bending stiffness, axial-and transversal forces as well as for initial conditions to be irregular functions or distributions. We prove the well-posedness of this problem in the very weak sense. More precisely, we define the very weak solution to the problem and show its existence and uniqueness. For regular enough coefficients we show consistency with the weak solution. Numerical analysis shows that the very weak solution coincides with the weak solution, when the latter exists, but also offers more insights into the behaviour of the very weak solution, when the weak solution doesn’t exist.}},
author = {{Blommaert, Robin and Lazendic, Srdan and Oparnica, Ljubica}},
issn = {{0898-1221}},
journal = {{COMPUTERS & MATHEMATICS WITH APPLICATIONS}},
keywords = {{Differential equations with discontinuous coefficients,Very weak solutions to partial differential equations,Functional analytic methods,Energy estimates,WAVE-EQUATION,GENERALIZED SOLUTIONS,WEAK SOLUTIONS}},
language = {{eng}},
pages = {{171--183}},
title = {{The Euler-Bernoulli equation with distributional coefficients and forces}},
url = {{http://doi.org/10.1016/j.camwa.2022.08.011}},
volume = {{123}},
year = {{2022}},
}
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