The well-posedness of shock solutions to non-isentropic Euler-Poisson system with varying background charges. (English) Zbl 1467.35249
Summary: In this paper, the non-isentropic Euler-Poisson system with the varying background charges in flat nozzles is investigated. Under physically acceptable boundary conditions, we establish the monotonicity between shock location and the density at the exit of the nozzle. Moreover, the unique existence of the transonic shock solution is obtained.
MSC:
| 35Q31 | Euler equations |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35Q81 | PDEs in connection with semiconductor devices |
| 35B35 | Stability in context of PDEs |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 76H05 | Transonic flows |
| 76L05 | Shock waves and blast waves in fluid mechanics |
| 78A30 | Electro- and magnetostatics |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
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