scholarly journals Stochastic diffusion equation with singular diffusivity and gradient-dependent noise in binary tomography

2014 ◽  
Vol 542 ◽  
pp. 012001 ◽  
Author(s):  
B Sixou ◽  
L Wang ◽  
F Peyrin
Keyword(s):  
Diffusion Equation ◽  
Stochastic Diffusion ◽  
Stochastic Diffusion Equation ◽  
Binary Tomography ◽  
Singular Diffusivity

scholarly journals Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Jia Mu ◽  
Jiecuo Nan ◽  
Yong Zhou
Keyword(s):  
Brownian Motion ◽  
Diffusion Equation ◽  
Periodic Solutions ◽  
Fractional Brownian Motion ◽  
Stochastic Diffusion ◽  
Stochastic Diffusion Equation ◽  
Asymptotically Periodic ◽  
Existence And Stability ◽  
The Fixed Point Theorem ◽  
Asymptotically Periodic Solutions

In this paper, a generalized Gronwall inequality is demonstrated, playing an important role in the study of fractional differential equations. In addition, with the fixed-point theorem and the properties of Mittag–Leffler functions, some results of the existence as well as asymptotic stability of square-mean S-asymptotically periodic solutions to a fractional stochastic diffusion equation with fractional Brownian motion are obtained. In the end, an example of numerical simulation is given to illustrate the effectiveness of our theory results.

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