Stability on large non-constant steady states of semiconductor equations. (English) Zbl 1467.82098
Summary: Around the large non-constant steady state, we show the existence and uniqueness of the global solution of the three-dimensional Cauchy problem of the semiconductor equations without or with the magnetic field effect. Without the magnetic field effect, we prove that the solution converges to the non-constant steady state exponentially fast as time goes to infinity. With the magnetic field effect, the optimal algebraic time-decay rates of the lower-order derivatives of the solution are obtained. Our results manifest that the degenerate dissipation of the magnetic field slows down the decay rates of the whole solution.
©2021 American Institute of Physics
©2021 American Institute of Physics
MSC:
| 82D37 | Statistical mechanics of semiconductors |
| 35Q81 | PDEs in connection with semiconductor devices |
| 35B35 | Stability in context of PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 78A25 | Electromagnetic theory (general) |
| 78A30 | Electro- and magnetostatics |
| 76N06 | Compressible Navier-Stokes equations |
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