TY - JOUR
T1 - Self-similar solutions of the Euler equations with spherical symmetry
AU - Peng, Chen Chang
AU - Lien, Wen Ching
N1 - Funding Information:
The authors would like to thank Prof. M-H. Chen for helpful discussions and the programming of the numerical solutions. Lien was supported in part by NSC Grant 97-2115-M-006-012 .
PY - 2012/11
Y1 - 2012/11
N2 - We consider self-similar flows arising from the uniform expansion of a spherical piston and preceded by a shock wave front. With appropriate boundary conditions imposed on the piston surface and the spherical shock, the isentropic compressible Euler system is transformed into a nonlinear ODE system. We formulate the problem in a simple form in order to present the analytic proof of the global existence of positive smooth solutions.
AB - We consider self-similar flows arising from the uniform expansion of a spherical piston and preceded by a shock wave front. With appropriate boundary conditions imposed on the piston surface and the spherical shock, the isentropic compressible Euler system is transformed into a nonlinear ODE system. We formulate the problem in a simple form in order to present the analytic proof of the global existence of positive smooth solutions.
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U2 - 10.1016/j.na.2012.07.019
DO - 10.1016/j.na.2012.07.019
M3 - Article
AN - SCOPUS:84865336175
SN - 0362-546X
VL - 75
SP - 6370
EP - 6378
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 17
ER -