Regularity and uniqueness of solutions to a parabolic system in nonequilibrium thermodynamics

Nonlinear Analysis, Theory, Methods and Applications

Volumn 41, Issue 5, 2000, Pages 669-688

  Jüngel, Ansgar ^a,b  

^a UNIVERSITY OF ROSTOCK   (Germany)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CARRIER CONCENTRATION; DIFFERENTIAL EQUATIONS; ELECTRIC POTENTIAL; ELECTRON ENERGY LEVELS; ELECTRONS; GREEN'S FUNCTION; INTEGRAL EQUATIONS; SEMICONDUCTOR MATERIALS; THEOREM PROVING; THERMODYNAMIC PROPERTIES;

NONEQUILIBRIUM THERMODYNAMICS; PARABOLIC SYSTEM; SEMIDISCRETIZATION OF TIME; SPATIAL AND TEMPORAL REGULARITY; UNIQUENESS OF WEAK SOLUTIONS;

NONLINEAR EQUATIONS;

EID: 0034251770     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00303-4     Document Type: Article

References (33)

1. G. Albinus, A thermodynamically motivated formulation of the energy model of semiconductor devices, preprint No. 210, Weierstrass-Institut, Berlin, Germany.
2. H. Alt, S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983) 311-341.
3. 2, p-regularity for solutions of mixed problems, J. Math. Pures Appl. 53 (1974) 279-290.
4. N. Ben Abdallah, P. Degond, On a hierarchy of macroscopic models for semiconductors, J. Math. Phys. 37 (1996) 3308-3333.
5. N. Ben Abdallah, L. Desvillettes, S. Génieys, On the convergence of the Boltzmann equation for semiconductors towards an energy transport model, 1998, submitted for publication.
6. N. Ben Abdallah, P. Degond, S. Génieys, An energy-transport model for semiconductors derived from the Boltzmann equation, J. Statist. Phys. 84 (1996) 205-231.
7. A. Bermudez, C. Saguez, Mathematical formulation and numerical solution of an alloy solidification problem, in: A. Fasano (Ed.), Free Boundary Problems: Theory and Applications, vol. 1, Pitman, London, 1983, pp. 237-247.
8. H. Brézis, Analyse Fonctionelle, Masson, Paris, 1994.
9. Y. Choi, R. Lui, Multi-dimensional electrochemistry model, Arch. Rat. Mech. Anal. 130 (1995) 315-342.
10. P. Degond, S. Génieys, A. Jüngel, An existence result for a strongly coupled parabolic system arising in nonequilibrium thermodynamics, C. R. Acad. Sci. Paris 325 (1997) 227-232.
11. P. Degond, S. Génieys, A. Jüngel, A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects, J. Math. Pures Appl. 76 (1997) 991-1015.
12. P. Degond, S. Génieys, A. Jüngel, A steady-state system in nonequilibrium thermodynamics including thermal and electrical effects, Math. Meth. Appl. Sci. (1998), in press.
13. P. Degond, C. Schmeiser, Macroscopic models for semiconductor heterostructures, Preprint No. 97.25, Université Paul Sabatier, Toulouse, France, 1997.
14. Z. Deyl (Ed.), Electrophoresis: A Survey of Techniques and Applications, Elsevier, Amsterdam, 1979.
15. E. DiBenedetto, Degenerate Parabolic Equations, Springer, New York, 1993.
16. J. Filo, J. Kačur, Local existence of general nonlinear parabolic systems, Nonlinear Anal. 24 (1995) 1597-1618.
17. S. Génieys, Energy-transport model for a non degenerate semiconductor, Convergence of the Hubert expansion in the linearized case, Asympt. Anal. (1998), in press.
18. M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton University Press, Princeton, 1983.
19. D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, Berlin, 1983.
20. P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman, Boston, 1985.
21. 1, p-estimate for solutions to mixed boundary value problems for second order elliptic differential equations, Math. Ann. 283 (1989) 679-687.
22. S. De Groot, Thermodynamik irreversibler Prozesse, Bibliographisches Institut, Mannheim, 1960.
23. S. De Groot, P. Mazur, Non-Equilibrium Thermodynamics, Dover, New York, 1984.
24. R. Hills, D.Loper, P. Roberts, A thermodynamically consistent model of a mushy zone, Quart. J. Mech. Appl. Math. 36 (1983) 505-539.
25. J. Jerome, Approximation of Nonlinear Evolution Systems, Academic Press, New York, 1983.
26. O. John, J. Stará, On the regularity and non-regularity of elliptic and parabolic systems, in: J. Kurzweil (Ed.), Equadiff 7, Teubner-Texte Math., vol. 118, Teubner, Leipzig, 1990, pp. 28-36.
27. A. Jüngel, Stationary transport equations for charge carriers in semiconductors including electron-hole scattering, Appl. Anal. 62 (1996) 53-69.
28. H. Kreuzer, Nonequilibrium Thermodynamics and its Statistical Foundation, Clarendon Press, Oxford, 1981.
29. q estimate on weak solutions of nonlinear elliptic systems, Dipartimento di Matematica, Université di Catania, Italy, preprint.
30. 1-contraction and uniqueness for quasilinear elliptic-parabolic equations, J. Differential Equations 131 (1996) 20-38.
31. P(0, T;B), Ann. Math. Pura Appl. 146 (1987) 65-96.
32. J. Stará, O. John, J. Malý, Counterexample to the regularity of weak solutions of the quasilinear parabolic system, Comment. Math. Univ. Carolin. 27 (1986) 123-136.
33. G.M. Troianiello, Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987.