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DOI:http://dx.doi.org/10.26855/jamc.2022.03.007

Global Existence and Stability of Time-Periodic Solution to 1-D Isentropic Compressible Euler Equations with Source Term

Date: February 24,2022 |Hits: 920 Download PDF How to cite this paper

Xiaomin Zhang

Department of Mathematics, Shandong Normal University, Jinan 250014, Shandong, China.

*Corresponding author: Xiaomin Zhang

Abstract

In this paper, we study the global existence and stability of time-periodic solution to 1-D isentropic compressible Euler equations with a source term α(t)ρu near the subsonic background solution . We first introduce the Riemann invariants to transform equations to a symmetrical system, and then rewrite the dominating equations which indicate the difference between Riemann invariant and background subsonic solution. For the proof of the existence and stability of time-periodic solutions, we all use the iterative method. Since we consider the subsonic flow, we need to the left and right boundary conditions. When proving the existence, we transform the boundary value problem into two initial value problems and the linearized system is now decoupled in each iteration. For the isothermal compressible Euler equations, we can also prove the global existence and stability of time-periodic solution of initial-boundary problem in the same way as this paper. The proof process will not be described in detail.

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How to cite this paper

Global Existence and Stability of Time-Periodic Solution to 1-D Isentropic Compressible Euler Equations with Source Term

How to cite this paper: Xiaomin Zhang. (2022) Global Existence and Stability of Time-Periodic Solution to 1-D Isentropic Compressible Euler Equations with Source Term. Journal of Applied Mathematics and Computation6(1), 41-52.

DOI: http://dx.doi.org/10.26855/jamc.2022.03.007

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