Abstract
Travelling wave solutions with shock profile for a one-dimensional model system associated with compressible viscous gas are investigated in terms of asymptotic stability. The travelling wave solution is proved to be asymptotically stable, provided the initial disturbance is suitably small and of zero constant component. The proof is given by the elementalL 2 energy method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. M. Ilin and O. A. Oleinik, Asymptotic behavior of the solutions of the Cauchy problem for certain quasilinear equations for large time (Russian). Math. USSR-Sb.,51 (1960), 191–216.
N. Itaya, A survey on two model equations for compressible viscous fluid. J. Math. Kyoto Univ.,19 (1979), 293–300.
S. Kawashima and T. Nishida, Global solutions to the initial value problem for the equations of one-dimensional motion of viscous polytropic gases. J. Math. Kyoto Univ.,21 (1981), 825–837.
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases. J. Math. Kyoto Univ.,20 (1980), 67–104.
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids. Proc. Japan Acad. Ser. A,55 (1979), 337–342.
T. Nishida and J. A. Smoller, Solutions in the large for some nonlinear hyperbolic conservation laws. Comm. Pure Appl. Math.,26 (1973), 183–200.
A. I. Vol’pert and Hujaev, On the Cauchy problem for composite systems of nonlinear differential equations. Math USSR-Sb.,16 (1972), 517–544.
Author information
Authors and Affiliations
About this article
Cite this article
Matsumura, A., Nishihara, K. On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas. Japan J. Appl. Math. 2, 17–25 (1985). https://doi.org/10.1007/BF03167036
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF03167036