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Symmetries and Large Time Asymptotics of Compressible Euler Flows with Damping
Author(s) -
Sachdev P. L.,
Mayil Vaganan B.,
Sivagami G.
Publication year - 2008
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2007.00397.x
Subject(s) - polytropic process , euler equations , mathematics , semi implicit euler method , mathematical analysis , partial differential equation , ordinary differential equation , nonlinear system , differential equation , euler method , first order partial differential equation , compressibility , backward euler method , classical mechanics , physics , mechanics , quantum mechanics
Large time asymptotics of compressible Euler equations for a polytropic gas with and without the porous media equation are constructed in which the Barenblatt solution is embedded. Invariance analysis for these governing equations are carried out using the classical and the direct methods. A new second order nonlinear partial differential equation is derived and is shown to reduce to an Euler–Painlevé equation. A regular perturbation solution of a reduced ordinary differential equation is determined. And an exact closed form solution of a system of ordinary differential equations is derived using the invariance analysis.