On the controllability of the non-isentropic 1-D Euler equation
نویسنده
چکیده
In this paper, we examine the question of the boundary controllability of the one-dimensional nonisentropic Euler equation for compressible polytropic gas, in the context of weak entropy solutions. We consider the system in Eulerian coordinates and the one in Lagrangian coordinates. We obtain for both systems a result of controllability toward constant states (with the limitation γ < 5 3 on the adiabatic constant for the Lagrangian system). The solutions that we obtain remain of small total variation in space if the initial condition is itself of sufficiently small total variation.
منابع مشابه
A controllability result for the 1-D isentropic Euler equation
In the above equation, t is the time x is the position, ρ = ρ(t, x) ≥ 0 is the density of the fluid, m(t, x) is the momentum (v(t, x) = m(t,x) ρ(t,x) is the velocity of the fluid), the pressure law is p(ρ) = κρ γ , γ ∈ (1, 3]. Equation (EI) is formulated in Eulerian coordinates. The problem of one-dimensional isentropic gas dynamics is also frequently studied in Lagrangian coordinates: { ∂tτ − ...
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