Asymptotic behavior of subsonic entropy solutions of the isentropic Euler-Poisson equations

The hydrodynarnic model for semiconductors in one dimension is considered. For perturbated Riemann data, global subsonic (weak) entropy solutions, piecewise continuous and piecewise smooth solutions with shock discontinuities are constructed and their asymptotic behavior is analyzed. In subsonic domains, the solution is smooth and, exponentially as t → ∞, tends to the corresponding stationary solution due to the influence of Poisson coupling. Along the shock discontinuity, the shock strength and the difference of derivatives of solutions decay exponentially affected by the relaxation mechanism.