scholarly journals Difference schemes for weak solutions of mixed problem for a class of parabolic differential equations I.

2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Hoàng Đình Dũng ◽  
Vũ Thế Ngọc
Keyword(s):  
Differential Equations ◽  
Mixed Problem ◽  
Weak Solutions ◽  
Difference Schemes ◽  
Parabolic Differential Equations

scholarly journals Finite Difference Schemes for Partial Differential Equations with Weak Solutions and Irregular Coefficients

2004 ◽  
Vol 4 (1) ◽  
pp. 48-65 ◽  
Author(s):  
Boško S. Jovanović
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Sobolev Space ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Weak Solutions ◽  
Difference Schemes ◽  
Generalized Solutions ◽  
Finite Difference Schemes ◽  
Singular Coefficients

AbstractA survey of the results concerning the convergence of finite difference schemes for boundary value problems with generalized solutions from the Sobolev space is presented. In particular, difference schemes for some problems with singular coefficients are investigated.

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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