M. Motamed, F. Nobile, R. Tempone, **Analysis and Computation of Hyperbolic PDEs with Random Data**, Encyclopedia of Applied and Computational Mathematics, pp 51-58, November 2015

M. Motamed, F. Nobile, R. Tempone

Analysis and Computation of Hyperbolic PDEs with Random Data

2015

Hyperbolic
partial differential equations (PDEs) are mathematical models of wave
phenomena, with applications in a wide range of scientific and
engineering fields such as electromagnetic radiation, geosciences, fluid
and solid mechanics, aeroacoustics, and general relativity. The theory
of hyperbolic problems, including Friedrichs and Kreiss theories, has
been well developed based on energy estimates and the method of Fourier
and Laplace transforms [8, 16]. Moreover, stable numerical methods, such as the finite difference method [14], the finite volume method [17], the finite element method [6], the spectral method [4], and the boundary element method [11],
have been proposed to compute approximate solutions of hyperbolic
problems. However, the development of the theory and numerics for
hyperbolic PDEs has been based on the assumption that all input data,
such as coefficients, initial data, boundary and force terms, and
computational domain, are *exactly known*.

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DOI 10.1007/978-3-540-70529-1_527