Free boundary problem from stochastic lattice gas model

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1. [1] M. Bramson and J.L. Lebowitz, Asymptotic behavior of densities for two-particle annihilating random walks, J. Statis. Phys.62 (1991) 297-372. Zbl0739.60091MR1105266
2. [2] G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rat. Mech. Anal.92 (1986) 205-245. Zbl0608.35080MR816623
3. [3] L. Chayes and G. Swindle, Hydrodynamic limits for one-dimensional particle systems with moving boundaries, Ann. Probab.24 (1996) 559-598. Zbl0869.60085MR1404521
4. [4] W.H. Fleming and M. Viot, Some measure-valued Markov processes in population genetics theory, Indiana Univ. Math. J.28 (1979) 817-943. Zbl0444.60064MR542340
5. [5] A. Friedman, Variational Principles and Free-Boundary Problems, Wiley, New York, 1982. Zbl0564.49002MR679313
6. [6] T. Funaki, K. Handa and K. Uchiyama, Hydrodynamic limit of one-dimensional exclusion processes with speed change, Ann. Probab.19 (1991) 245- 265. Zbl0725.60114MR1085335
7. [7] T. Funaki, K. Uchiyama and H.T. Yau, Hydrodynamic limit for lattice gas reversible under Bernoulli measures, in: T. Funaki and W.A. Woyczynski (Eds.), Nonlinear Stochastic PDE's: Hydrodynamic Limit and Burgers' Turbulence, IMA, Vol. 77, Univ. Minnesota, Springer, 1995, pp. 1-40. Zbl0840.60091MR1395890
8. [8] T. Funaki and H. Spohn, Motion by mean curvature from the Ginzburg-Landau ∇φ-interface model, Commun. Math. Phys.185 (1997) 1-36. Zbl0884.58098MR1463032
9. [9] H.O. Georgii, Canonical Gibbs Measures, Lect. Notes in Math., Vol. 760, Springer, 1979. Zbl0409.60094MR551621
10. [10] M.Z. Guo, G.C. Papanicolaou and S.R.S. Varadhan, Nonlinear diffusion limit for a system with nearest neighbor interactions, Commun. Math. Phys.118 (1988) 31-59. Zbl0652.60107MR954674
11. [11] C. Landim, S. Olla and S. Volchan, Driven tracer particle in one dimensional symmetric simple exclusion, Commun. Math. Phys.192 (1998) 287-307. Zbl0911.60085MR1617558
12. [12] F. Rezakhanlou, Hydrodynamic limit for attractive particle systems on Zd, Commun. Math. Phys.140 (1991) 417-448. Zbl0738.60098MR1130693
13. [13] J.-F. Rodrigues, Variational methods in the Stefan problem, in: A. Visintin (Ed.), Phase Transitions and Hysteresis, Lect. Notes in Math., Vol. 1584, Springer, 1994, pp. 147-212. Zbl0819.35154MR1321833
14. [14] L.I. Rubinstein, The Stefan Problem, Amer. Math. Soc. Transl. Monogr.27, Providence, 1971. Zbl0219.35043
15. [15] A.A. Samarskii and E.S. Nikolaev, Numerical Methods for Grid Equations, Vol. I, Birkhäuser, 1989. Zbl0649.65054MR1004468
16. [16] H. Spohn, Large Scale Dynamics of Interacting Particles, Springer, 1991. Zbl0742.76002
17. [17] H. Spohn, Interface motion in models with stochastic dynamics, J. Statis. Phys.71 (1993) 1081-1132. Zbl0935.82546MR1226387
18. [18] Y. Suzuki and K. Uchiyama, Hydrodynamic limit for a spin system on a multidimensional lattice, Probab. Theory Related Fields95 (1993) 47-74. Zbl0794.60099MR1207306
19. [19] K. Uchiyama, Scaling limits of interacting diffusions with arbitrary initial distributions, Probab. Theory Related Fields99 (1994) 97-110. Zbl0801.60092MR1273743
20. [20] S.R.S. Varadhan, Scaling limits for interacting diffusions, Commun. Math. Phys.135 (1991) 313-353. Zbl0725.60085MR1087387