Global Weak Solutions to the Cauchy Problem for a Two-Phase Model at a Node

2020 ◽  
Vol 52 (2) ◽  
pp. 1567-1590
Author(s):  
Mauro Garavello ◽  
Francesca Marcellini
Keyword(s):  
Cauchy Problem ◽  
Weak Solutions ◽  
Phase Model ◽  
Global Weak Solutions ◽  
Two Phase ◽  
The Cauchy Problem

scholarly journals TheH1(R)Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Zhaowei Sheng ◽  
Shaoyong Lai ◽  
Yuan Ma ◽  
Xuanjun Luo
Keyword(s):  
Cauchy Problem ◽  
Weak Solutions ◽  
Space Variable ◽  
Global Weak Solutions ◽  
Initial Value ◽  
Dissipative Term ◽  
First Order ◽  
Holm Equation ◽  
The Cauchy Problem ◽  
Derivatives Of

The existence of global weak solutions to the Cauchy problem for a generalized Camassa-Holm equation with a dissipative term is investigated in the spaceC([0,∞)×R)∩L∞([0,∞);H1(R))provided that its initial valueu0(x)belongs to the spaceH1(R). A one-sided super bound estimate and a space-time higher-norm estimate on the first-order derivatives of the solution with respect to the space variable are derived.

Weak solutions to a hydrodynamic model for semiconductors: the Cauchy problem

1995 ◽  
Vol 125 (1) ◽  
pp. 115-131 ◽  
Author(s):  
Pierangelo Marcati ◽  
Roberto Natalini
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Existence Theorem ◽  
Weak Solutions ◽  
Hydrodynamic Model ◽  
Fractional Step ◽  
Large Initial Data ◽  
Global Weak Solutions ◽  
The Cauchy Problem

We investigate the Cauchy problem for a hydrodynamic model for semiconductors. An existence theorem of global weak solutions with large initial data is obtained by using the fractional step Lax—Friedrichs scheme and Godounov scheme.

Smoothing effect on the damping mechanism for an inviscid two-phase gas—liquid model

2014 ◽  
Vol 144 (2) ◽  
pp. 351-362 ◽  
Author(s):  
Lizhi Ruan
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
External Force ◽  
Smooth Solution ◽  
Smoothing Effect ◽  
Two Phase ◽  
Global Smooth Solution ◽  
Liquid Model ◽  
The Cauchy Problem

In this paper, we consider the Cauchy problem for an inviscid two-phase gas—liquid model with external force, in order to demonstrate the smoothing effect on the damping mechanism. It is shown that the Cauchy problem admits a unique global smooth solution provided that the initial data are smooth and the C0-norm of the derivative of the initial data are small.

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