Time-Periodic Isentropic Supersonic Euler flows in One-Dimensional Ducts Driving by Periodic Boundary Conditions
- 1 Downloads
We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws.
Key wordssupersonic flow isentropic compressible Euler equations duct time-periodic solution initial-boundary-value problem
2010 MR Subject Classification35B10 35L04 76G20
Unable to display preview. Download preview PDF.
- Matsumura A, Nishida T. Periodic solutions of a viscous gas equation//Recent Topics in Nonlinear PDE, IV (Kyoto, 1988). North-Holland Math Stud 160. Amsterdam: North-Holland, 1989: 49–82Google Scholar
- Glimm J, Lax P D. Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the American Mathematical Society, 1970, (101)Google Scholar