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Well‐posedness of the Hydrodynamic Model for Semiconductors
Author(s) -
Yeh LiMing
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199612)19:18<1489::aid-mma848>3.0.co;2-x
Subject(s) - mathematics , dissipative system , mathematical analysis , boundary value problem , dirichlet boundary condition , hyperbolic partial differential equation , boundary (topology) , partial differential equation , physics , quantum mechanics
This paper concerns the well‐posedness of the hydrodynamic model for semiconductor devices, a quasi‐linear elliptic–parbolic–hyperbolic system. Boundary conditions for elliptic and parabolic equations are Dirichlet conditions while boundary conditions for the hyperbolic equations are assumed to be well‐posed in L 2 sense. Maximally strictly dissipative boundary conditions for the hyperbolic equations satisfy the assumption of well‐posedness in L 2 sense. The well‐posedness of the model under the boundary conditions is demonstrated.