From Diffusion to Reaction via Γ-Convergence (original) (raw)

Abstract

The singular limit is analysed by means of Gamma-convergence in the space of finite Borel measures endowed with the weak-* topology.

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References (17)

  1. S. Adams, N. Dirr, M. A. Peletier, and J. Zimmer. Foundation of the Wasserstein gradient-flow formulation of diffusion: A large-deviation approach. In preparation.
  2. L. Ambrosio, N. Gigli, and G. Savaré. Gradient Flows in Metric Spaces and in the Space of Probability Measures. Lectures in mathematics ETH Zürich. Birkhäuser, 2005.
  3. R. Aris. Mathematical Modeling: A Chemical Engineer's Perspective. Academic Press, 1999.
  4. H. Attouch. Variational convergence for functions and operators. Pitman (Advanced Publishing Program), Boston, MA, 1984.
  5. H. Brezis. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North Holland, 1973.
  6. H. Brezis. Analyse fonctionelle -Théorie et applications. Collection Mathématiques appliquées pour la maîtrise. Masson, first edition, 1983.
  7. G. Da Prato and A. Lunardi. On a class of self-adjoint elliptic operators in L 2 spaces with respect to invariant measures. J. Differential Equations, 234(1):54-79, 2007.
  8. G. Dal Maso. An introduction to Γ-convergence, volume 8 of Progress in Nonlinear Differential Equations and Their Applications. Birkhäuser, Boston, first edition, 1993.
  9. P. Érdi and J. Tóth. Mathematical Models of Chemical Reactions: Theory and Applica- tions of Deterministic and Stochastic Models. Manchester University Press, 1989.
  10. J. E. Hutchinson. Second fundamental form for varifolds and the existence of surfaces minimising curvature. Indiana Univ. Math. J., 35:45-71, 1986.
  11. R. Jordan, D. Kinderlehrer, and F. Otto. The variational formulation of the Fokker- Planck Equation. SIAM Journal on Mathematical Analysis, 29(1):1-17, 1998.
  12. H. A. Kramers. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica, 7(4):284-304, 1940.
  13. J. Lions and E. Magenes. Non Homogeneous Boundary Value Problems and Applications, volume I. Springer, New York-Heidelberg, 1972.
  14. A. Mielke. Energy-drift-diffusion equations with recombination as entropy-gradient sys- tem. In preparation, 2009.
  15. F. Otto. The geometry of dissipative evolution equations: The porous medium equation. Comm. PDE, 26:101-174, 2001.
  16. M. Pennacchio, G. Savaré, and P. Colli Franzone. Multiscale modeling for the bioelectric activity of the heart. SIAM J. Math. Anal., 37(4):1333-1370 (electronic), 2005.
  17. J. G. Rešetnjak. The weak convergence of completely additive vector-valued set functions. Sibirsk. Mat. Z., 9:1386-1394, 1968.