scholarly journals The Global Existence and Uniqueness of the Classical Solution with the Periodic Initial Value Problem for One-Dimension Klein-Gordon-Zakharov Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Cong Sun ◽  
Lixia Li
Keyword(s):  
Global Existence ◽  
Galerkin Method ◽  
Classical Solution ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
One Dimension ◽  
Global Classical Solution ◽  
Initial Value ◽  
Klein Gordon ◽  
Global Existence And Uniqueness

Through applying Galerkin method, we establish the approximating solution for one-dimension Klein-Gordon-Zakharov equations and obtain the local classical solution. By applying integral estimates, we also obtain the existence and uniqueness of the global classical solution of Klein-Gordon-Zakharov equations.

scholarly journals Existence and Uniqueness of Solutions for a Type of Generalized Zakharov System

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Rui Li ◽  
Xing Lin ◽  
Zongwei Ma ◽  
Jingjun Zhang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Energy Conservation ◽  
Classical Solution ◽  
Sobolev Spaces ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Zakharov System ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We study the Cauchy problem for a type of generalized Zakharov system. With the help of energy conservation and approximate argument, we obtain global existence and uniqueness in Sobolev spaces for this system. Particularly, this result implies the existence of classical solution for this generalized Zakharov system.

scholarly journals Global existence of strong solutions for incompressible hydrodynamic flow of liquid crystals with vacuum

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1247-1257 ◽  
Author(s):  
Shijin Ding ◽  
Jinrui Huang ◽  
Fengguang Xia
Keyword(s):  
Cauchy Problem ◽  
Liquid Crystals ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Strong Solutions ◽  
Hydrodynamic Flow ◽  
Three Dimensions ◽  
Small Initial Data ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We consider the Cauchy problem for incompressible hydrodynamic flow of nematic liquid crystals in three dimensions. We prove the global existence and uniqueness of the strong solutions with nonnegative p0 and small initial data.

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

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