Solution of the cauchy problem for a plane one-dimensional isentropic gas flow in a constant gravitational field

1975 ◽  
Vol 15 (3) ◽  
pp. 143-150
Author(s):  
V.I. Golin'ko
Keyword(s):  
Cauchy Problem ◽  
Gravitational Field ◽  
Gas Flow ◽  
One Dimensional ◽  
The Cauchy Problem ◽  
Isentropic Gas

scholarly journals Global existence of small amplitude solutions to one-dimensional nonlinear Klein–Gordon systems with different masses

2015 ◽  
Vol 12 (04) ◽  
pp. 745-762 ◽  
Author(s):  
Donghyun Kim
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Small Amplitude ◽  
Space Dimension ◽  
Structural Condition ◽  
Cauchy Data ◽  
One Dimensional ◽  
Compactly Supported ◽  
The Cauchy Problem ◽  
Klein Gordon

We study the Cauchy problem for systems of cubic nonlinear Klein–Gordon equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the rate [Formula: see text] in [Formula: see text], [Formula: see text] as [Formula: see text] tends to infinity even in the case of mass resonance, if the Cauchy data are sufficiently small, smooth and compactly supported.

The global Hölder-continuous solution of isentropic gas dynamics

1993 ◽  
Vol 123 (2) ◽  
pp. 231-238 ◽  
Author(s):  
Yun-Guang Lu
Keyword(s):  
Cauchy Problem ◽  
Gas Dynamics ◽  
Continuous Solution ◽  
Hölder Continuous ◽  
Vanishing Viscosity ◽  
Equations Of Gas Dynamics ◽  
The Cauchy Problem ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

SynopsisThis paper considers the Cauchy problem for the isentropic equations of gas dynamics in Euler coordinates ρt + (ρu)x = 0, (ρu)t + (ρu)2 + P(ρ))x=0 and gives the Hölder-continuous solution by applying the method of vanishing viscosity.

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