A sequence of integro-differential equations approximating a viscous porous medium equation

Zeitschrift für Analysis und ihre Anwendungen

Volumn 20, Issue 1, 2001, Pages 55-91

  Oelschlager K ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

Asymptotic expansions; Integro differential equations; Porous medium equations

Indexed keywords

EID: 25944476744     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. Adams, R. A.: Sobolev Spaces. New York: Academic Press 1975.
2. Buttà, P. and J. L. Lebowitz: Hydrodynamic limit of Brownian particles interacting with short- and long-range forces. J. Stat. Phys. 94 (1999), 653-694.
3. Caffarelli, L. A. and C. E. Kenig: Gradient estimates for variable coefficient parabolic equations and singular perturbation problems. Amer. J. Math. 120 (1998), 391-439.
4. Fabes, E. B.: Gaussian upper bounds on fundamental solutions of parabolic equations; the method of Nash. Led. Notes Math. 1563 (1993).
5. Friedman, A.: Partial Differential Equations of Parabolic Type. Malabar (Florida, USA): Robert E. Krieger Publ. Comp. 1983.
6. Gärtner, J.: On the McKean-Vlasov limit for interacting diffusions. Math. Nachr. 137 (1988), 197-248.
7. Kipnis, C. and C. Landim: Scaling Limits of Interacting Particle Systems. Berlin: Springer-Verlag 1999.
8. Ladyženskaja, O. A., Solonnikov, V. A. and N. N. Ural'ceva: Linear and Quasi-Linear Equations of Parabolic Type (Translations of Mathematical Monographs: Vol. 23). Providence (R.I.): Amer. Math. Soc. 1968.
9. Oelschläger, K.: A law of large numbers for moderately interacting diffusion processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 69 (1985), 279-322.
10. Oelschläger, K.: A fluctuation theorem for moderately interacting diffusion processes. Probab. Theory Rel. Fields 74 (1987), 591-616.
11. Oelschläger, K.: On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes. Probab. Theory Rel. Fields 82 (1989), 565-586.
12. Oelschläger, K.: On the connection between Hamillonian many-particle systems and the hydrodynamical equations. Arch. Rat. Mech. Anal. 115 (1991), 297-310.
13. Oelschläger, K.: The description of many-particle systems by the equations for a viscous, compressible, barotropic fluid. Math. Models Methods Appl. Sci. 5 (1995), 887-922.
14. Oelschläger, K.: An integro-differential equation modelling a Newtonian dynamics and its scaling limit. Arch. Rat. Mech. Anal. 137 (1997), 99-134.
15. Oelschläger, K.: Simulation of the solution of a viscous porous medium equation by a particle method. Preprint 1998.
16. Varadhan, S. R. S.: Scaling limits for interacting diffusions. Comm. Math. Phys. 135 (1991), 313-353.