Cauchy-Kovalevsky theorems for hyperbolic systems of conservation laws with piecewise analytic initial data

1987 ◽  
pp. 43-50
Author(s):  
Eduard Harabetian
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Systems Of Conservation Laws

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.

GRADIENT DRIVEN AND SINGULAR FLUX BLOWUP OF SMOOTH SOLUTIONS TO HYPERBOLIC SYSTEMS OF CONSERVATION LAWS

2004 ◽  
Vol 01 (04) ◽  
pp. 627-641 ◽  
Author(s):  
HELGE KRISTIAN JENSSEN ◽  
ROBIN YOUNG
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Finite Time ◽  
Hyperbolic Systems ◽  
Shock Formation ◽  
Smooth Solutions ◽  
Flux Function ◽  
Systems Of Conservation Laws ◽  
Blowup In Finite Time

We consider two new classes of examples of sup-norm blowup in finite time for strictly hyperbolic systems of conservation laws. The explosive growth in amplitude is caused either by a gradient catastrophe or by a singularity in the flux function. The examples show that solutions of uniformly strictly hyperbolic systems can remain as smooth as the initial data until the time of blowup. Consequently, blowup in amplitude is not necessarily strictly preceded by shock formation.

scholarly journals On the uniqueness of solutions to hyperbolic systems of conservation laws

2021 ◽  
Vol 291 ◽  
pp. 110-153
Author(s):  
Shyam Sundar Ghoshal ◽  
Animesh Jana ◽  
Konstantinos Koumatos
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Uniqueness Of Solutions ◽  
Systems Of Conservation Laws
Sign in / Sign up

Export Citation Format

Share Document