The semidiscrete damped wave equation with a fractional Laplacian
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- by Carlos Lizama and Marina Murillo-Arcila
- Proc. Amer. Math. Soc. 151 (2023), 1987-1999
- DOI: https://doi.org/10.1090/proc/16231
- Published electronically: February 28, 2023
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Abstract:
In this paper we completely solve the open problem of finding the fundamental solution of the semidiscrete fractional-spatial damped wave equation. We combine operator theory and Laplace transform methods with properties of Bessel functions to show an explicit representation of the solution when initial conditions are given. Our findings extend known results from the literature and also provide new insights into the qualitative behavior of the solutions for the studied model. As an example, we show the existence of almost periodic solutions as well as their profile in the homogeneous case.References
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Bibliographic Information
- Carlos Lizama
- Affiliation: Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago, Chile
- MR Author ID: 114975
- ORCID: 0000-0002-9807-1100
- Email: carlos.lizama@usach.cl
- Marina Murillo-Arcila
- Affiliation: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, Spain
- MR Author ID: 998995
- ORCID: 0000-0001-6589-0452
- Email: mamuar1@upv.es
- Received by editor(s): July 12, 2022
- Received by editor(s) in revised form: August 10, 2022, and August 12, 2022
- Published electronically: February 28, 2023
- Additional Notes: The first author was partially supported by ANID Project Fondecyt 1220036 and Generalitat Valenciana, Project PROMETEU/2021/070. The second author was supported by MCIN/AEI/10.13039/501100011033, Project PID2019-105011GB-I00, and by Generalitat Valenciana, Project PROMETEU/2021/070.
- Communicated by: Ariel Barton
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 1987-1999
- MSC (2020): Primary 35R11; Secondary 39A06, 26A33, 44A10
- DOI: https://doi.org/10.1090/proc/16231
- MathSciNet review: 4556194