Scaling limits for time-fractional diffusion-wave systems with random initial data

Gi-Ren Liu, Narn Rueih Shieh

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let w (x, t) := (u, v)(x, t), x ∈ ℝ3, t > 0, be the ℝ2-valued spatial-temporal random field w = (u, v) arising from a certain two-equation system of time-fractional linear partial differential equations of reaction-diffusion-wave type, with given random initial data u(x,0), ut(x,0), and v(x,0), vt(x,0). We discuss the scaling limit, under proper homogenization and renormalization, of w(x,t), subject to suitable assumptions on the random initial conditions. Since the component fields u,v depend on the interactions present within the system, we employ a certain stochastic decoupling method to tackle this component dependence. The work shows, in particular, the various non-Gaussian scenarios proposed in [4, 13, 17] and the references therein, for the single diffusion type equations, in classical or in fractional time/space derivatives, can be studied for the two-equation system, in a significant way.

Original languageEnglish
Pages (from-to)1-35
Number of pages35
JournalStochastics and Dynamics
Volume10
Issue number1
DOIs
Publication statusPublished - 2010 Mar 1

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Fractional Diffusion
Scaling Limit
Fractional
Linear partial differential equation
Reaction-diffusion
Decoupling
Homogenization
Renormalization
Random Field
Partial differential equations
System of equations
Initial conditions
Derivatives
Derivative
Scenarios
Interaction

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation

Cite this

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Scaling limits for time-fractional diffusion-wave systems with random initial data. / Liu, Gi-Ren; Shieh, Narn Rueih.

In: Stochastics and Dynamics, Vol. 10, No. 1, 01.03.2010, p. 1-35.

Research output: Contribution to journalArticle

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