Asymptotic Analysis II —: Surveys and New Trends by Z. Schuss, B. J. Matkowsky (auth.), F. Verhulst (eds.)

By Z. Schuss, B. J. Matkowsky (auth.), F. Verhulst (eds.)

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17. , Persistence of dynamical systems under random perturbations, SIAM Rev. 17 (1975), pp. 605-640. 18. Matkowsky, B. , "Singular Perturbations and Asymptotics," Ed. R. E. Meyer and S. V. Parter, Acad. Press (1980), pp. 109-146. 19. Matkowsky, B. J. and Z. Schuss, The exit problem for randomly perturbed dynamical systems, SlAM J. Appl. Math. 33 (1977), pp. 365-382. 20. , Eigenvalues of the Fokker-Planck operator and the approach to equilibrium for diffusions in potential fields, loc. cit. 40 (2) (1981), pp.

Andquantitative (1973), Perturbations optimal, (1974), bolic differential Applics. of arbitrary problems order; aux 323, Springer- have been considered Singular perturbation operators can be found in dans les probl~mes Lecture Notes Math. Higher order operators Besjes results singuli~res by for linear para- J. Math. Anal. 48, 594-609 This paper studies the equation ~u/~t + eLlu + L0u = f with L I, L 0 linear elliptic partial differential operators; order 2m, L 0 is of lower order and the spatial variables L 1 is of are restrict- ed to a bounded domain in ~n.

6. Note that p(x,ylx,~) is essentially The mean lifetime of meta-stable the Boltzmann density about independent (x0,O) (x,y). 17) or by the equation x + Bx + U'(x) = 0 where U(x) = - Ix - cos x. Here I is the constant driving current, and the voltage V across the junction is given by V = = lim ~1 T÷~ IT ~(t)dt 0 The constant 8 is related to resistance and other parameters of the junction [27]. 1) is identical to that of the damped physical pendulum driven by a constant torque I. 1) for which i is function of x.

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