Diffusion approximation for the linear Boltzmann equation of semiconductor theory with analysis of the initial layer

Journal of Mathematical Analysis and Applications

Volumn 205, Issue 1, 1997, Pages 216-238

  Banasiak, J ^a  

^a UNIVERSITY OF KWAZULU NATAL   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; DIFFUSION; HYDRODYNAMICS; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS;

DIFFUSION APPROXIMATION; LINEAR BOLTZMANN EQUATION;

APPROXIMATION THEORY;

EID: 0030609329     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.5164     Document Type: Article

References (18)

1. Arlotti L. The Cauchy problem for the linear Maxwell-Boltzmann equation. J. Differential Equations. 69:1987;166-184.
2. J. Banasiak, 1995, Singular perturbations of resonance type with applications to the kinetic theory, Proceedings of the Conference on Evolution Equations, Glasgow, 1994, Longman, Harlow.
3. Banasiak J. Asymptotic analysis of abstract linear kinetic equation. Math. Methods Appl. Sci. 19:1996;481-505.
4. J. Banasiak, G. Frosali, 1994, Modified Chapman-Enskog Expansion for an Electron Transport Equation with a Constant Electric Field, Universitá degli Studi di Ancona, Luglio.
5. Banasiak J., Mika J. R. Asymptotic analysis of the Fokker-Planck equation of Brownian motion. Math. Mod. Methods Appl. Sci. 4:1994;17-33.
6. Banasiak J., Mika J. R. Diffusion limit for the linear Boltzmann equation of the neutron transport theory. Math. Methods Appl. Sci. 17:1994;1071-1087.
7. Bardos C., Santos R., Sentis R. Diffusion approximation and computation of the critical size. Trans. Amer. Math. Soc. 284:1984;617-649.
8. Degond P., Mas-Gallic S. Existence of solutions and diffusion approximation for a model Fokker-Planck equation. Transport. Theory Statist. Phys. 16:1987;589-639.
9. Frosali G., van der Mee C. V. M., Paveri-Fontana S. L. Conditions for runaway phenomena in the kinetic theory of particle swarms. J. Math. Phys. 30:1989;1177-1186.
10. Larsen E. W., Keller J. B. Asymptotic solution of neutron transport problems for small mean free paths. J. Math. Phys. 15:1974;75-81.
11. Markowich P. A., Ringhofer C. A., Schmeiser C. Semiconductor Equations. 1989;Springer-Verlag, New York.
12. Mika J. R. New asymptotic expansion algorithm for singularly perturbed evolution equations. Math. Methods Appl. Sci. 3:1981;172-188.
13. Mika J. R., Banasiak J. Asymptotic analysis of a model kinetic equation. Math. Mod. Methods Appl. Sci. 5:1995;867-885.
14. Mika J. R., Banasiak J. Singularly Perturbed Evolution Equations with Applications to Kinetic Theory. 1995;World Scientific, Singapore.
15. Nagel R. One-Parameter Semigroups of Positive Operators. Lecture Notes in Mathematics. 1184:1986;Springer-Verlag, Berlin/Heidelberg.
16. Poupaud F. Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers. Asymptotic Anal. 4:1991;293-317.
17. Poupaud F. Runaway phenomena and fluid approximation under high fields in semiconductor kinetic theory. Z. Angew. Math. Mech. 72:1992;359-372.
18. Schaefer H. H. Topological Vector Spaces. 1980;Springer-Verlag, New York.