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 -