scholarly journals Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics

1996 ◽  
Vol 177 (2) ◽  
pp. 349-380 ◽  
Author(s):  
E Weinan ◽  
Yu. G. Rykov ◽  
Ya. G. Sinai
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Weak Solutions ◽  
Variational Principles ◽  
Particle Dynamics ◽  
Global Weak Solutions ◽  
Random Initial Data ◽  
Systems Of Conservation Laws ◽  
Generalized Variational Principles ◽  
And Behavior

A BOUNDED VARIATION ESTIMATE FOR THE FORCE SCHEME APPLIED TO STRICTLY HYPERBOLIC SYSTEMS OF CONSERVATION LAWS IN THE TEMPLE CLASS

2013 ◽  
Vol 10 (01) ◽  
pp. 105-127
Author(s):  
RAJIB DUTTA
Keyword(s):  
Probability Theory ◽  
Initial Data ◽  
Conservation Laws ◽  
Random Walks ◽  
Total Variation ◽  
Bounded Variation ◽  
Hyperbolic Systems ◽  
Godunov Scheme ◽  
Systems Of Conservation Laws ◽  
The Temple

Bressan and Jenssen established a uniform bounded variation (BV) estimate for the Godunov scheme for Temple-type strictly hyperbolic systems of conservation laws and gave a proof based on the probability theory of random walks. In this paper, we provide a different proof which is simpler and does not use any probability theory. Applying our theory, we establish a uniform BV estimate for the Force scheme for the same class of hyperbolic systems, under the assumption of small total variation of initial data.

Existence of the solutions for the Ginzburg–Landau equations of superconductivity in three spatial dimensions

1999 ◽  
Vol 129 (3) ◽  
pp. 627-639 ◽  
Author(s):  
Bixiang Wang ◽  
Ning Su
Keyword(s):  
Initial Data ◽  
Weak Solutions ◽  
Time Dependent ◽  
Global Weak Solutions ◽  
Ginzburg Landau ◽  
Spatial Dimensions ◽  
Ginzburg Landau Equations

The time-dependent Ginzburg-Landau equations of superconductivity in three spatial dimensions are investigated in this paper. We establish the existence of global weak solutions for this model with any Lp (p ≧ 3) initial data. This work generalizes the results of Wang and Zhan.

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