scholarly journals Several Dynamical Properties for a Nonlinear Shallow Water Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ls Yong ◽  
Haibo Yan
Keyword(s):  
Shallow Water ◽  
Natural Number ◽  
Weak Solutions ◽  
Shallow Water Equation ◽  
Type Estimate ◽  
Third Order ◽  
Existence Of Weak Solutions ◽  
Dynamical Properties

A nonlinear third order dispersive shallow water equation including the Degasperis-Procesi model is investigated. The existence of weak solutions for the equation is proved in the spaceL1(R)∩BV (R)under certain assumptions. The Oleinik type estimate andL2N(R)  (Nis a natural number) estimate for the solution are obtained.

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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