On the mean square stability of a class of nonstationary coupled partial differential equations

1979 ◽  
Vol 48 (4) ◽  
pp. 213-219 ◽  
Author(s):  
G. Ahmadi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mean Square ◽  
Partial Differential ◽  
Coupled Partial Differential Equations ◽  
Mean Square Stability ◽  
The Mean

AN AVERAGING PRINCIPLE FOR TWO-SCALE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

2011 ◽  
Vol 11 (02n03) ◽  
pp. 353-367 ◽  
Author(s):  
HONGBO FU ◽  
JINQIAO DUAN
Keyword(s):  
Dynamical System ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Slow Component ◽  
Averaging Principle ◽  
Fast Time ◽  
Mean Square ◽  
Partial Differential ◽  
The Mean

Multiscale stochastic partial differential equations arise as models for various complex systems. An averaging principle for a class of stochastic partial differential equations with slow and fast time scales is established. Under suitable conditions, it is shown that the slow component converges to an effective dynamical system in the mean-square uniform sense.

scholarly journals Fractional-in-time and multifractional-in-space stochastic partial differential equations

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Vo V. Anh ◽  
Nikolai N. Leonenko ◽  
María D. Ruiz-Medina
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
White Noise ◽  
Stochastic Partial Differential Equations ◽  
Pseudodifferential Operators ◽  
Weak Sense ◽  
Variable Order ◽  
Mean Square ◽  
Partial Differential ◽  
The Mean

AbstractThis paper derives the weak-sense Gaussian solution to a family of fractional-in-time and multifractional-in-space stochastic partial differential equations, driven by fractional-integrated-in-time spatiotemporal white noise. Some fundamental results on the theory of pseudodifferential operators of variable order, and on the Mittag-Leffler function are applied to obtain the temporal, spatial and spatiotemporal Hölder continuity, in the mean-square sense, of the derived solution.

scholarly journals On the solution of reaction-diffusion equations with double diffusivity

1987 ◽  
Vol 10 (1) ◽  
pp. 163-172
Author(s):  
B. D. Aggarwala ◽  
C. Nasim
Keyword(s):  
Heat Conduction ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Partial Differential ◽  
Coupled Partial Differential Equations ◽  
Special Cases ◽  
Two Temperatures

In this paper, solution of a pair of Coupled Partial Differential equations is derived. These equations arise in the solution of problems of flow of homogeneous liquids in fissured rocks and heat conduction involving two temperatures. These equations have been considered by Hill and Aifantis, but the technique we use appears to be simpler and more direct, and some new results are derived. Also, discussion about the propagation of initial discontinuities is given and illustrated with graphs of some special cases.

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