scholarly journals An Empirical Interpolation and Model-Variance Reduction Method for Computing Statistical Outputs of Parametrized Stochastic Partial Differential Equations

2016 ◽  
Vol 4 (1) ◽  
pp. 244-265 ◽  
Author(s):  
F. Vidal-Codina ◽  
N. C. Nguyen ◽  
M. B. Giles ◽  
J. Peraire
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Variance Reduction ◽  
Reduction Method ◽  
Partial Differential

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

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