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We consider two classes of quasi-linear parabolic equations depending on a small parameter ε. The asymptotic behavior of the solutions as t → α and ε → 0 is investigated by studying the associated Markov family. We find its dependence on the way t and ε-1 go to infinity and on the initial point.
Keywords: asymptotic behavior, quasi-linear equation, Markov families, fluctuations, dynamical systems
