On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity

Mishura, Yuliya; Ralchenko, Kostiantyn; Zili, Mounir

doi:10.1016/j.spl.2019.108682

Cited by 2 publications

(1 citation statement)

References 7 publications

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“…The problem of stochastic partial differential equations (SPDEs) driven by this Gaussian process has been widely studied during the past two decades. Here, we only list some recent results [7][8][9]15,16,22].…”

Section: Introductionmentioning

confidence: 99%

Decompositions of stochastic convolution driven by a white-fractional Gaussian noise

Wang

Zhang

2021

Front. Math. China

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Let u = {u(t, x); (t, x) ∈ R + × R} be the solution to a linear stochastic heat equation driven by a Gaussian noise, which is a Brownian motion in time and a fractional Brownian motion in space with Hurst parameter H ∈ (0, 1). For any given x ∈ R (resp., t ∈ R + ), we show a decomposition of the stochastic process t → u(t, x) (resp., x → u(t, x)) as the sum of a fractional Brownian motion with Hurst parameter H/2 (resp., H) and a stochastic process with C ∞ -continuous trajectories. Some applications of those decompositions are discussed.

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Section: Introductionmentioning

confidence: 99%

Decompositions of stochastic convolution driven by a white-fractional Gaussian noise

Wang

Zhang

2021

Front. Math. China

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A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise

2020

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A spectral collocation approach is constructed to solve a class of time-fractional stochastic heat equations (TFSHEs) driven by Brownian motion. Stochastic differential equations with additive noise have an important role in explaining some symmetry phenomena such as symmetry breaking in molecular vibrations. Finding the exact solution of such equations is difficult in many cases. Thus, a collocation method based on sixth-kind Chebyshev polynomials (SKCPs) is introduced to assess their numerical solutions. This collocation approach reduces the considered problem to a system of linear algebraic equations. The convergence and error analysis of the suggested scheme are investigated. In the end, numerical results and the order of convergence are evaluated for some numerical test problems to illustrate the efficiency and robustness of the presented method.

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On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity

Cited by 2 publications

References 7 publications

Decompositions of stochastic convolution driven by a white-fractional Gaussian noise

Decompositions of stochastic convolution driven by a white-fractional Gaussian noise

A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise

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