MR2197537 Iwata, Yoritaka and Yamamoto, Yoshitaka Yoritaka IWATA and Yoshitaka YAMAMOTO A Model for the Jeans Instability in One-Dimensional Motion of Compressible Viscous Gases Funkcialaj Ekvacioj. Serio Internacia 48 2005 415--451 http://fe.math.kobe-u.ac.jp/FE/FullPapers/48-3/48_415.pdf http://www.ams.org/mathscinet-getitem?mr=MR2197537 The Jeans instability is an astrophysical idea associated with the collapse of a fluctuated infinite homogeneous self-gravitating gas. If a fluctuation ideally takes the form of a plane wave, then the growth of the wavelength is a factor of the instability. As a model we consider a system of equations describing the one-dimensional periodic motion of a self-gravitating viscous gas. Concerning the model system we study the structure of the whole stationary solutions, the asymptotic behavior of solutions, and the nonlinear stability of stationary solutions. The Jeans instability is closely related with bifurcation of solutions in the stationary problem of the model system. The Jeans instability, Self-Gravitating viscous gas, Bifurcation of stationary solutions, Stability of stationary solutions. 76E20, 76N15. 48-415 2005 A Model for the Jeans Instability in One-Dimensional Motion of Compressible Viscous Gases Yoritaka IWATA and Yoshitaka YAMAMOTO Yoritaka IWATA and Yoshitaka YAMAMOTO 1 Antontsev, S. N.; Kazhikhov, A. V.; Monakhov, V. N. Boundary Value Problems in Mechanics of Nonhomogeneous Fluids North-Holland, Amsterdam 1990 MR1035212 2 Binney, J.; Tremaine, S. Galactic Dynamics Princeton University Press, Princeton 1987
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