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Global existence of smooth solutions of the $$N$$-dimensional Euler-Poisson model. (English) Zbl 1043.35109
A semiconductor model consistent with extended thermodynamics is considered. The Cauchy problem is studied under the assumption that initial data are close to a steady-state solution. The global unique solvability is proved, and the exponential stability of the steady-state solution is established. The question of the momentum relaxation time limit $$\tau\to 0$$ is studied with the condition $$\tau\sigma \to\beta$$, $$\beta =\text{const}>0$$, where $$\sigma$$ is the energy relaxation time.

##### MSC:
 35L65 Hyperbolic conservation laws 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 35M10 PDEs of mixed type 35B40 Asymptotic behavior of solutions to PDEs 82D37 Statistical mechanical studies of semiconductors
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