A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 64, Issue 1, 2013, Pages 29-52

  Glitzky, Annegret ^a   Mielke, Alexander ^a  

^a WIAS Berlin   (Germany)

Author keywords

Electro reaction diffusion systems; Free energy functional; Gradient flow evolution; Interface kinetics; Reversible mass action type reactions

Indexed keywords

DIFFUSION IN LIQUIDS; DYNAMIC MODELS; FREE ENERGY;

ENERGY FUNCTIONALS; GRADIENT FLOW; INTERFACE KINETICS; MASS ACTION; REACTION DIFFUSION SYSTEMS;

REACTION KINETICS;

EID: 84873524513     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-012-0207-y     Document Type: Article

References (27)

1. Albinus G., Gajewski H., Hünlich R.: Thermodynamic design of energy models of semiconductor devices. Nonlinearity 15(2), 367-383 (2002).
2. Bandelow U., Gajewski H., Hünlich R.: Fabry-perot lasers: thermodynamics based modeling. In: Piprek, J. (ed) Optoelectronic Devices: Advanced Simulation and Analysis, pp. 63-85. Springer, Berlin (2005).
3. Bandelow U., Hünlich R., Koprucki T.: Simulation of static and dynamic properties of edge-emitting multiple-quantum-well lasers. IEEE J. Sel. Top. Quantum Electron. 9, 798-806 (2003).
4. Desvillettes L., Fellner K.: Exponential decay toward equilibrium via entropy methods for reaction-diffusion equations. J. Math. Anal. Appl. 319, 157-176 (2006).
5. De Groot S., Mazur P.: Non-Equilibrium Thermodynamics. Dover, New York, NY (1984).
6. Érdi P., Tóth J.: Mathematical Models of Chemical Reactions. Theory and Applications of Deterministic and Stochastic Models. Princeton University Press, Princeton, NJ (1989).
7. Feinberg M., Horn F. J. M.: Chemical mechanism structure and the coincidence of the stoichiometric and kinetic subspaces. Arch. Ration. Mech. Anal. 66(1), 83-97 (1977).
8. Gajewski H., Gröger K.: Initial boundary value problems modelling heterogeneous semiconductor devices. In: Schulze, B.-W., Triebel, H. (eds) Surveys on Analysis, Geometry and Mathematical Physics, vol. 117 of Teubner-Texte zur Mathematik, pp. 4-53. Teubner, Leipzig (1990).
9. Gajewski H., Gröger K.: Reaction-diffusion processes of electrically charged species. Math. Nachr. 177, 109-130 (1996).
10. Glitzky A., Gröger K., Hünlich R.: Free energy and dissipation rate for reaction diffusion processes of electrically charged species. Appl. Anal. 60, 201-217 (1996).
11. Glitzky A., Gärtner K.: Energy estimates for continuous and discretized electro-reaction-diffusion systems. Nonlinear Anal. 70, 788-805 (2009).
12. Glitzky A., Hünlich R.: Energetic estimates and asymptotic for electro-reaction-diffusion systems. Z. angew. Math. Mech. 77(11), 823-832 (1997).
13. Glitzky A.: Analysis of a spin-polarized drift-diffusion model. Adv. Sci. Appl. 18, 401-427 (2008).
14. Glitzky A.: Exponential decay of the free energy for discretized electro-reaction-diffusion systems. Nonlinearity 21, 1989-2009 (2008).
15. Glitzky A.: Energy estimates for electro-reaction-diffusion systems with partly fast kinetics. Discret. Continuous Dyn. Syst. A 25, 159-174 (2009).
16. Glitzky A.: Uniform exponential decay of the free energy for Voronoi finite volume discretized reaction-diffusion systems. Math. Nachr. 284, 2159-2174 (2011).
17. Glitzky A.: Analysis of electronic models for solar cells including energy resolved defect densities. Math. Methods Appl. Sci. 34, 1980-1998 (2011).
18. Glitzky, A.: An electronic model for solar cells including active interfaces and energy resolved defect densities. WIAS preprint 1663 (2011, submitted).
19. Gröger K.: Asymptotic behavior of solutions to a class of diffusion-reaction equations. Math. Nachr. 112, 19-33 (1983).
20. Jordan R., Kinderlehrer D., Otto F.: The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29(1), 1-17 (1998).
21. Mielke A.: A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems. Nonlinearity 24, 1329-1346 (2011).
22. Mielke, A.: Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions. Discret. Continuous Dyn. Syst. Ser. S. WIAS preprint 1661 (2012, to appear).
23. Otto F.: Dynamics of labyrinthine pattern formation in magnetic fluids: a mean-field theory. Arch. Ration. Mech. Anal. 141(1), 63-103 (1998).
24. Otto F.: The geometry of dissipative evolution equations: the porous medium equation. Commun. Partial Differ. Equ. 26, 101-174 (2001).
25. Stangl R., Leendertz C., Haschke J.: Numerical simulation of solar cells and solar cell characterization methods: the open-source on demand program AFORS-HET. In: Rugescu, R. D. (ed) Solar Energy, pp. 319-352. INTECH, Croatia (2010).
26. Vlad M. O., Ross J.: Thermodynamically based constraints for rate coefficients of large biochemical networks. WIREs Syst. Biol. Med. 1, 348-358 (2009).
27. Wegscheider R.: Über simultane Gleichgewichte und die Beziehungen zwischen Thermodynamik und Reaktionskinetik homogener Systeme. Z. Phys. Chemie 39, 257-303 (1902).