From diffusion to reaction via γ-convergence

SIAM Journal on Mathematical Analysis

Volumn 42, Issue 4, 2010, Pages 1805-1825

  Peletier, Mark A ^a   Savaré, Giuseppe ^b   Veneroni, Marco ^c  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF PAVIA   (Italy)

^c TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Activation energy; Dirichlet forms; High energy limit; Mosco convergence; Scale bridging; Unification; Upscaling; Variational evolution equations

Indexed keywords

DIRICHLET FORM; EVOLUTION EQUATIONS; HIGH-ENERGY LIMIT; MOSCO-CONVERGENCE; SCALE-BRIDGING; UNIFICATION; UPSCALING;

BIOLOGY; BROWNIAN MOVEMENT; DIFFUSION; EQUATIONS OF MOTION; FOKKER PLANCK EQUATION; HIGH ENERGY PHYSICS; PROBABILITY DENSITY FUNCTION; SELF ASSEMBLY;

ACTIVATION ENERGY;

EID: 77956080212     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/090781474     Document Type: Article

References (18)

1. S. Adams, N. Dirr, M. A. Peletier, and J. Zimmer, From a large-deviations principle to the Wasserstein gradient flow: A new micro-macro passage, preprint, available online from http://arxiv.org/abs/1004.4076, 2010.
2. L. Ambrosio, N. Gigli, and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures, Lectures in Math. ETH Zürich, Birkhäuser, Basel, 2005.
3. R. Aris, Mathematical Modeling: A Chemical Engineer's Perspective, Academic Press, New York, 1999.
4. H. Attouch, Variational Convergence for Functions and Operators, Applicable Mathematics Series, Pitman (Advanced Publishing Program), Boston, 1984.
5. H. Brezis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam, 1973.
6. H. Brezis, Analyse fonctionnelle: Théorie et applications, Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, 1983.
7. G. Da Prato and A. Lunardi, On a class of self-adjoint elliptic operators in L2 spaces with respect to invariant measures, J. Differential Equations, 234 (2007), pp. 54-79.
8. G. Dal Maso, An Introduction to Γ-Convergence, Progr. Nonlinear Differential Equations Appl. 8, Birkhäuser Boston, Boston, 1993.
9. P. Érdi and J. Tóth, Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models, Manchester University Press, Manchester, UK, 1989.
10. J. E. Hutchinson, Second fundamental form for varifolds and the existence of surfaces minimising curvature, Indiana Univ. Math. J., 35 (1986), pp. 45-71.
11. R. Jordan, D. Kinderlehrer, and F. Otto, The variational formulation of the Fokker- Planck Equation, SIAM J. Math. Anal., 29 (1998), pp. 1-17.
12. H. A. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions, Phys., 7 (1940), pp. 284-304.
13. J. Lions and E. Magenes, Non Homogeneous Boundary Value Problems and Applications, Volume I, Springer, New York, Heidelberg, 1972.
14. A. Mielke, A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems, Technical report 1485, WIAS, Berlin, 2010.
15. U. Mosco, Approximation of the solutions of some variational inequalities, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3), 21 (1967), pp. 373-394.
16. F. Otto, The geometry of dissipative evolution equations: The porous medium equation, Comm. Partial Differential Equations, 26 (2001), pp. 101-174.
17. M. Pennacchio, G. Savaré, and P. Colli Franzone, Multiscale modeling for the bioelectric activity of the heart, SIAM J. Math. Anal., 37 (2006), pp. 1333-1370.
18. J. G. Rešetnjak, The weak convergence of completely additive vector-valued set functions, Sibirsk. Mat. Ž., 9 (1968), pp. 1386-1394.