Global Existence of Shock Front Solution to 1-D Piston Problem for Compressible Euler Equations

2018 ◽  
Vol 20 (4) ◽  
pp. 2053-2071
Author(s):  
Min Ding
Keyword(s):  
Global Existence ◽  
Shock Front ◽  
Euler Equations ◽  
Compressible Euler Equations ◽  
Piston Problem ◽  
Front Solution ◽  
Compressible Euler ◽  
Shock Front Solution

GLOBAL EXISTENCE OF SHOCK FRONT SOLUTIONS TO THE AXIALLY SYMMETRIC PISTON PROBLEM FOR COMPRESSIBLE FLUIDS

2004 ◽  
Vol 01 (01) ◽  
pp. 51-84 ◽  
Author(s):  
SHUXING CHEN ◽  
ZEJUN WANG ◽  
YONGQIAN ZHANG
Keyword(s):  
Global Existence ◽  
Shock Front ◽  
Compressible Fluids ◽  
Axially Symmetric ◽  
Piston Problem ◽  
Front Solution ◽  
Glimm Scheme ◽  
Front Solutions ◽  
Shock Front Solution

In this paper, we study the axially symmetric piston problem for compressible fluids when the velocity of the piston is a perturbation of a constant. Under the assumptions that both the velocity of the piston and the density of the gas outside the piston are small, we prove the global existence of a shock front solution by using a modified Glimm scheme.

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