Small random perturbations of infinite dimensional dynamical systems and nucleation theory

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1. [1] W.G. Faris and G. Jona-Lasinio, Large fluctuations for a non linear heat equation with noise. J. Phys. A : Math. Gen., t. 15, 1982, p. 3025-3055. Zbl0496.60060MR684578
2. [2] G. Parisi and Y.S. Wu, Scienta Sinica, t. 24, 1981, p. 483-496. MR626795
3. [3] J.L. Lebowitz and O. Penrose, Toward a rigorous molecular theory of metastability. In Fluctuation Phenomena. Studies in Statistical Mechanics, edited by J. L. Lebowitz and E. W. Montroll. Amsterdam, North Holland, 1979. MR578729
4. [4] J. Sewel, Stability Equilibrium and Metastability in Statistical Mechanics. Phys. Rep., t. 57, 1980, p. 307. MR556940
5. [5] M. Cassandro, A. Galves, E. Olivieri and M.E. Vares, Metastability behaviour of Stochastic Dynamics: a pathwise approach. J. Stat. Phys., t. 35, 1984, p. 603-634. Zbl0591.60080MR749840
6. [6] A. Galves, E. Olivieri and M.E. Vares, Metastability for a class of dynamical systems subject to small random perturbations. Preprint I. H. E. S. Octobre 1984. Zbl0709.60058MR905332
7. [7] A.D. Wentzel and M.L. Freidlin, On small random perturbations of dynamical systems, Russian Math. Survey, t. 25, 1, 1970, p. 1-55. Some problems concerning stability under small random perturbations. Theory of Probability and Appl., t. 17, 2, 1972, p. 269-283. Zbl0297.34053MR267221
8. [8] M.L. Freidlin and A.D. Wentzel, Random perturbations of dynamical system. Springer Verlag. New-York, Berlin, Heidelberg, Tokyo, 1984. MR722136
9. [9] C.L. Thompson, Mathematical statistical mechanics. Princeton University, Press1972. Zbl0244.60082
10. [10] T.H. Eisele and R.S. Ellis, Symmetry breaking and random waves for magnetic systems on a circle. Wahrscheinlichkeitstheorie Verw. Geb., t. 63, 1983, p 297-348. Zbl0494.60097MR705628
11. [11] W.S. Loud, Periodic Solution of x'' + cx' + g(x) = ∈f(t). Memoirs of the American Mathematical Society, n° 31, 1959. Zbl0085.30701MR107058
12. [12] N. Chafee and E. Infante, A bifurcation problem for a non linear parabolic equation. J. Applicable Anal., t. 4, 1974, p. 17-37. Zbl0296.35046MR440205
13. [13] D. Henry, Geometric theory of Semilinear Parabolic equation. Lecture notes in Math., n° 840, Springer Verlag, Berlin, Heidelbérg, New York, 1981. Zbl0456.35001MR610244
14. [14] T. Laetsch, Critical solutions of autonomous non linear boundary value problems. Indiana University. Math. Journal, t. 24, n° 7, 1975, p. 651-658. Zbl0314.34065
15. [15] H. Berestycki, Le nombre de solutions de certains problèmes semi-linéaires elliptiques. J. of Functional Analysis, t. 40, 1981, p. 1-29. Zbl0452.35038MR607588
16. [16] E.A. Coddington and N. Levinson, Theory of ordinary differential equations. Mc Grawhill, New York, Toronto, London, 1955. Zbl0064.33002MR69338
17. [17] R. Courant and D. Hilbert, Methods of Methematical Physics. t. 1. Intersciences, New York, 1953. Zbl0051.28802MR65391

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