We study the effect of Gaussian perturbations on a hyperbolic partial differential equation with double characteristics in two spatial dimensions. The coefficients of our partial differential operator depend polynomially on the space variables, while the noise is additive, white in time and coloured in space. We provide a sufficient condition on the spectral measure of the covariance functional describing the noise that allows for the existence of a random field solution for the resulting stochastic partial differential equation. Our approach is based on explicit computations for the fundamental solution of the partial differential operator and its Fourier transform.

Bernardi E., Lanconelli A. (2023). On a Class of Stochastic Hyperbolic Equations with Double Characteristics. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 29(1), 1-16 [10.1007/s00041-022-09987-7].

On a Class of Stochastic Hyperbolic Equations with Double Characteristics

Bernardi E.
Primo
Investigation
;
Lanconelli A.
Secondo
Investigation
2023

Abstract

We study the effect of Gaussian perturbations on a hyperbolic partial differential equation with double characteristics in two spatial dimensions. The coefficients of our partial differential operator depend polynomially on the space variables, while the noise is additive, white in time and coloured in space. We provide a sufficient condition on the spectral measure of the covariance functional describing the noise that allows for the existence of a random field solution for the resulting stochastic partial differential equation. Our approach is based on explicit computations for the fundamental solution of the partial differential operator and its Fourier transform.
2023
Bernardi E., Lanconelli A. (2023). On a Class of Stochastic Hyperbolic Equations with Double Characteristics. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 29(1), 1-16 [10.1007/s00041-022-09987-7].
Bernardi E.; Lanconelli A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/909685
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