scholarly journals A Preconditioned Low-Rank Projection Method with a Rank-Reduction Scheme for Stochastic Partial Differential Equations

2017 ◽  
Vol 39 (5) ◽  
pp. S828-S850 ◽  
Author(s):  
Kookjin Lee ◽  
Howard C. Elman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Projection Method ◽  
Stochastic Partial Differential Equations ◽  
Low Rank ◽  
Reduction Scheme ◽  
Rank Reduction ◽  
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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