scholarly journals A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations

2013 ◽  
Vol 242 ◽  
pp. 753-776 ◽  
Author(s):  
Mulin Cheng ◽  
Thomas Y. Hou ◽  
Zhiwen Zhang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Time Dependent ◽  
Partial Differential ◽  
Orthogonal Method

scholarly journals Approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with memory

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3433-3442 ◽  
Author(s):  
Diem Huan ◽  
Ravi Agarwal ◽  
Hongjun Gao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Approximate Controllability ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Time Dependent ◽  
Nonlinear Stochastic System ◽  
Partial Differential ◽  
With Memory

We establish results concerning the approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with memory in Hilbert spaces. By using semigroup theory, stochastic analysis techniques and fixed point approach, we derive a new set of sufficient conditions for the approximate controllability of nonlinear stochastic system under the assumption that the corresponding linear system is approximately controllable. Further, the above results are generalized to cover a class of much more general impulsive neutral stochastic delay partial differential equations driven by L?vy noise in infinite dimensions. Finally, an example is provided to illustrate our results.

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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