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

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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Phys. Rev. B-6, 855 (1972). 36. Ben-Jacob, E. and Y, Imry (to appear). 37. Tesche, C. D. and J° J. Clarke, Low Temp. Phys. 29 (1977), p° 301. 38. Ben-Jacob, E. and Z. Schuss, The mean lifetime of the metastable states of the DC-SQUID and its I-V characteristics, Proc. 6th International Conf. S. special publication 614 (1981), p. 376. 39. Ohashi, K. and Ohashi, Y. , Nonlinear electrical transport in silver sulfide (to appear). 40. Murch, G. , Monte Carlo demonstration of solid state diffusion in an electric field, Am.

1. 0 Phase plane of the Josephson junction nonconstant periodic function of x. -Fig. 2). Thermal fluctuations in the Josephson junction have significant influence on the I-V response curve of the junction. 1). 6) x + Bx + U'(x) = / ~ k T so that the situation is identical with that of conductivity phenomena in ionic crystals [20] with the roles of current and voltage reversed [i]. 5 W2r Fig. 2. 6) in this case spends long time periods, T on the average, at the equilibrium points y = O, x = 2~rn + a r c s i n fluctuations.

A special p r o c e d u r e will be put forward in this case to smooth the b o u n d a r y layer functions a l l o w i n g us, with a certain accuracy, the construct an a s y m p t o t i c a p p r o x i m a t i o n of the solution which is u n i f o r m in ~. In section 1 we examine the first case for p r o b l e m (1-2), in section 2 we c o n s i d e r the analogous p r o b l e m in the case of two spatial variables. In section 3 we c o n s i d e r a q u a s i - l i n e a r system of parabolic equations which r e p r e s e n t s a model for certain problems kinetics.

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