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A viscous approximation for a 2‐D steady semiconductor or transonic gas dynamic flow: Existence theorem for potential flow
Author(s) -
Gamba Irene M.,
Morawetz Cathleen S.
Publication year - 1996
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199610)49:10<999::aid-cpa1>3.0.co;2-2
Subject(s) - transonic , poisson's equation , mathematics , streamlines, streaklines, and pathlines , boundary value problem , flow (mathematics) , partial differential equation , mathematical analysis , domain (mathematical analysis) , bounded function , physics , mechanics , geometry , aerodynamics
In this paper we solve a boundary value problem in a two‐dimensional domain O for a system of equations of Fluid‐Poisson type, that is, a viscous approximation to a potential equation for the velocity coupled with an ordinary differential equation along the streamlines for the density and a Poisson equation for the electric field. A particular case of this system is a viscous approximation of transonic flow models. The general case is a model for semiconductors. We show existence of a density ρ, velocity potential φ, and electric potential Φ in the bounded domain O that are C 1,α (O¯), C 2,α (O¯), and W 2,α (O¯) functions, respectively, such that ρ, φ, Φ, the speed |Δφ|, and the electric field E = ΔΦ are uniformly bounded in the viscous parameter. This is a necessary step in the existing programs in order to show existence of a solution for the transonic flow problem. © 1996 John Wiley & Sons, Inc.