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The global solution of initial-boundary value problem for Euler equations with damping. (English) Zbl 1052.35117

Summary: The initial-boundary value problem on the half-line for the isentropic Euler equations with damping is investigated in this paper. For homogeneous Dirichlet boundary condition, the existence and uniqueness of the global solution is obtained provided the initial data is a perturbation of the equilibrium solution. Moreover the solution tends to the equilibrium solution when \(t\to\infty\).

MSC:

35L50 Initial-boundary value problems for first-order hyperbolic systems
35L65 Hyperbolic conservation laws
35Q35 PDEs in connection with fluid mechanics
35B40 Asymptotic behavior of solutions to PDEs