Analysis of the random heat equation via approximate density functions
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Title
Analysis of the random heat equation via approximate density functionsDate
2021Publisher
Editura Academiei RomaneISSN
1221-1451Bibliographic citation
CALATAYUD, Julia; CORTÉS, J.C. Analysis of the random heat equation via approximate density functions. Romanian Reports in Physics, 2021, vol. 73, núm 2, p. 1-10Type
info:eu-repo/semantics/articlePublisher version
http://www.rrp.infim.ro/2021_73_2.htmlVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
In this paper we study the randomized heat equation with homo-
geneous boundary conditions. The diffusion coefficient is assumed to be a random
variable and the initial condition is treated as a stochastic process. ... [+]
In this paper we study the randomized heat equation with homo-
geneous boundary conditions. The diffusion coefficient is assumed to be a random
variable and the initial condition is treated as a stochastic process. The solution of
this randomized partial differential equation problem is a stochastic process, which is
given by a random series obtained via the classical method of separation of variables.
Any stochastic process is determined by its finite-dimensional joint distributions. In
this paper, the goal is to obtain approximations to the probability density function of
the solution (the first finite-dimensional distributions) under mild conditions. Since the
solution is expressed as a random series, we perform approximations to its probability
density function. Several illustrative examples are shown. [-]
Is part of
Romanian Reports in Physics, 2021, vol. 73, núm. 2, p. 1-10Funder Name
Ministerio de Economía, Industria y Competitividad, Gobierno de España | Agencia Estatal de Investigación | Fondo Europeo de Desarrollo Regional
Project code
MTM2017–89664–P
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