On the random wave equation within the mean square context
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Title
On the random wave equation within the mean square contextDate
2022-02Publisher
American Institute of Mathematical Sciences (AIMS)Bibliographic citation
CALATAYUD, Julia; CORTÉS, Juan Carlos; JORNET, Marc. On the random wave equation within the mean square context. Discrete & Continuous Dynamical Systems-S, 2022, vol. 15, no 2, p. 409.Type
info:eu-repo/semantics/articleVersion
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Abstract
This paper deals with the random wave equation on a bounded domain with Dirichlet boundary conditions. Randomness arises from the velocity wave, which is a positive random variable, and the two initial conditions, ... [+]
This paper deals with the random wave equation on a bounded domain with Dirichlet boundary conditions. Randomness arises from the velocity wave, which is a positive random variable, and the two initial conditions, which are regular stochastic processes. The aleatory nature of the inputs is mainly justified from data errors when modeling the motion of a vibrating string. Uncertainty is propagated from these inputs to the output, so that the solution becomes a smooth random field. We focus on the mean square contextualization of the problem. Existence and uniqueness of the exact series solution, based upon the classical method of separation of variables, are rigorously established. Exact series for the mean and the variance of the solution process are obtained, which converge at polynomial rate. Some numerical examples illustrate these facts. [-]
Is part of
Discrete & Continuous Dynamical Systems - S, February 2022, 15(2)Funder Name
Ministerio de Economía y Competitividad, España | Universitat Jaume I
Project code
PID2020–115270GB–I00
Project title or grant
postdoctoral contract , Acció 3.2 del Pla de Promoció de la Investigació de la Universitat Jaume I per a l'any 2020
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© 2022 American Institute of Mathematical Sciences
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