- -

On the random wave equation within the mean square context

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

On the random wave equation within the mean square context

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: CalatayudCortesJornet ...
Tamaño: 757.4Kb
Formato: PDF
Descripción: Versión del Autor.
Abrir
[Cerrado]
Nombre: DCDS_S_2022_Wave_ ...
Tamaño: 496.5Kb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor
dc.contributor.author Calatayud Gregori, Julia es_ES
dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author Jornet Sanz, Marc es_ES
dc.date.accessioned 2023-03-01T19:02:07Z
dc.date.available 2023-03-01T19:02:07Z
dc.date.issued 2022-02 es_ES
dc.identifier.issn 1937-1632 es_ES
dc.identifier.uri http://hdl.handle.net/10251/192204
dc.description.abstract [EN] 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. es_ES
dc.description.sponsorship This work has been partially supported by the Ministerio de Economia y Competitividad grant PID2020-115270GB-I00. Marc Jornet has been supported by a postdoctoral contract from Universitat Jaume I, Spain (Accio 3.2 del Pla de Promocio de la Investigacio de la Universitat Jaume I per a l'any 2020) es_ES
dc.language Inglés es_ES
dc.publisher American Institute of Mathematical Sciences es_ES
dc.relation.ispartof Discrete and Continuous Dynamical Systems. Series S es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Random wave partial differential equation es_ES
dc.subject Mean square calculus es_ES
dc.subject Exact series solution es_ES
dc.subject Separation of variables es_ES
dc.subject Mean and variance es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title On the random wave equation within the mean square context es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3934/dcdss.2021082 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-115270GB-I00/ES/ECUACIONES DIFERENCIALES ALEATORIAS. CUANTIFICACION DE LA INCERTIDUMBRE Y APLICACIONES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Facultad de Administración y Dirección de Empresas - Facultat d'Administració i Direcció d'Empreses es_ES
dc.description.bibliographicCitation Calatayud Gregori, J.; Cortés, J.; Jornet Sanz, M. (2022). On the random wave equation within the mean square context. Discrete and Continuous Dynamical Systems. Series S. 15(2):409-425. https://doi.org/10.3934/dcdss.2021082 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3934/dcdss.2021082 es_ES
dc.description.upvformatpinicio 409 es_ES
dc.description.upvformatpfin 425 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 15 es_ES
dc.description.issue 2 es_ES
dc.relation.pasarela S\438902 es_ES
dc.contributor.funder Universitat Jaume I es_ES
dc.contributor.funder AGENCIA ESTATAL DE INVESTIGACION es_ES
dc.description.references E. Allen, <i>Modeling With Itô Stochastic Differential Equations</i>, Springer Science &amp; Business Media, Dordrecht, Netherlands, 2007. es_ES
dc.description.references P. Almenar, L. Jódar, J. A. Martín.Mixed problems for the time-dependent telegraph equation: Continuous numerical solutions with a priori error bounds, <i>Mathematical and Computer Modelling</i>, <b>25</b> (1997), 31-44. es_ES
dc.description.references H. T. Banks, J. L. Davis, S. L. Ernstberger, S. Hu, E. Artimovich, A. K. Dhar, C. L. Browdy.A comparison of probabilistic and stochastic formulations in modelling growth uncertainty and variability, <i>Journal of Biological Dynamics</i>, <b>3</b> (2009), 130-148. es_ES
dc.description.references J. C. Cortés, P. Sevilla-Peris, L. Jódar.Analytic-numerical approximating processes of diffusion equation with data uncertainty, <i>Computers &amp; Mathematics with Applications</i>, <b>49</b> (2005), 1255-1266. es_ES
dc.description.references J. Calatayud, J. C. Cortés, M. Jornet.Uncertainty quantification for random parabolic equations with nonhomogeneous boundary conditions on a bounded domain via the approximation of the probability density function, <i>Mathematical Methods in the Applied Sciences</i>, <b>42</b> (2019), 5649-5667. es_ES
dc.description.references J. C. Cortés, L. Jódar, L. Villafuerte, F. J. Camacho.Random Airy type differential equations: Mean square exact and numerical solutions, <i>Computers and Mathematics with Applications</i>, <b>60</b> (2010), 1237-1244. es_ES
dc.description.references J. Calatayud, J. C. Cortés, M. Jornet.Computational uncertainty quantification for random non-autonomous second order linear differential equations via adapted gPC: A comparative case study with random Fröbenius method and Monte Carlo simulation, <i>Open Mathematics</i>, <b>16</b> (2018), 1651-1666. es_ES
dc.description.references S. J. Farlow, <i>Partial Differential Equations for Scientists and Engineers</i>, Dover, New York, 1993. es_ES
dc.description.references G. B. Folland, <i>Fourier Analysis and Its Applications</i>, Brooks, Pacific Grove, CA, Wadsworth, 1992. es_ES
dc.description.references E. A. González-Velasco., <i>Fourier Analysis and Boundary Value Problems</i>, <b>${ref.volume}</b> (1995). es_ES
dc.description.references G. R. Grimmet, D. R. Stirzaker., <i>Probability and Random Process</i>, <b>${ref.volume}</b> (2001). es_ES
dc.description.references D. Henderson and P. Plaschko, <i>Stochastic Differential Equations in Science and Engineering</i>, World Scientific, Singapore, 2006. es_ES
dc.description.references L. Jódar, P. Almenar.Accurate continuous numerical solutions of time dependent mixed partial differential problems, <i>Computers &amp; Mathematics with Applications</i>, <b>32</b> (1996), 5-19. es_ES
dc.description.references X. Mao, <i>Stochastic Differential Equations and Applications</i>, Elsevier, 2007. es_ES
dc.description.references T. Neckel and F. Rupp, <i>Random Differential Equations in Scientific Computing</i>, Walter de Gruyter, 2013. es_ES
dc.description.references F. Rodríguez, M. Roales, J. A. Martín.Exact solutions and numerical approximations of mixed problems for the wave equation with delay, <i>Applied Mathematics and Computation</i>, <b>219</b> (2012), 3178-3186. es_ES
dc.description.references S. Salsa, <i>Partial Differential Equations in Action, From Modelling to Theory</i>, Universitext, Springer-Verlag Italia, Milan, 2008. es_ES
dc.description.references T. T. Soong., <i>Random Differential Equations in Science and Engineering</i>, <b>${ref.volume}</b> (1973). es_ES
dc.description.references R. C. Smith, <i>Uncertainty Quantification: Theory, Implementation, and Applications</i>, SIAM, 2014. es_ES
dc.description.references L. Villafuerte, C. A. Braumann, J. C. Cortés, L. Jódar.Random differential operational calculus: Theory and applications, <i>Comput. Math. Appl.</i>, <b>59</b> (2010), 115-125. es_ES
dc.description.references D. Xiu., <i>Numerical Methods for Stochastic Computations: A Spectral Method Approach</i>, <b>${ref.volume}</b> (2010). es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem