Rothe's method for equations modelling transport of dopants in semiconductors.
- Glitzky, Annegret
- Gröger, Konrad
- Hünlich, Rolf
2010 Mathematics Subject Classification
- 35A40 35B40 35B45 35D05 35D10 35K57 65M99
- Transport of dopants in semiconductors, reaction-diffusion equations, Lyapunov function, a-priori estimates, global existence, asymptotic behaviour, discrete-time problems, convergence of Rothe's method, implicite and semi-implicite scheme
This paper is devoted to the investigation of some nonlinear reaction-diffusion system modelling the transport of dopants in semiconductors and arising in semiconductor technology. Besides of results on existence and qualitative properties of the solution to the problem itself we are interested in the investigation of corresponding discrete-time problems. Using Rothe's method in a fully implicite and a semi-implicite version, respectively, we get analogous results on existence and qualitative behaviour of solutions to the discrete-time equations. Moreover, convergence in some strong sense will be proved. Essential tools are estimates of the energy functional, L∞-estimates obtained by De Giorgi's method, Lq (S,W1,P )-estimates for the continuous problem as well as a discrete version of Gronwall's lemma.
- Nonlinear analysis, 28 (1997), pp. 463-487