An application of the Implicit Function Theorem to an energy model of the semiconductor theory
- Griepentrog, Jens André
2010 Mathematics Subject Classification
- 35B65 80A20 35D05 35D10 35J55
- Boundary value problems for elliptic systems, regularity of generalized solutions, heat and mass transfer, heat flow
In this paper we deal with a mathematical model for the description of heat conduction and carrier transport in semiconductor heterostructures. We solve a coupled system of nonlinear elliptic differential equations consisting of the heat equation with Joule heating as a source, the Poisson equation for the electric field an drift-diffusion equations with temperature dependent coefficients describing the charge and current conservation, subject to general thermal and electrical boundary conditions. We prove the existence and uniqueness of Hölder continuous weak solutions near thermodynamic equilibria points using the Implicit Function Theorem. To show the differentiability of maps corresponding to the weak formulation of the problem we use regularity results from the theory of nonsmooth linear elliptic boundary value problems in Sobolev-Campanato spaces.
- ZAMM Z. Angew. Math. Mech., 79 (1999) pp. 43--51.