On Stabilization of the Solutions of Parabolic Equations with Small Parameter

On Stabilization of the Solutions of Parabolic Equations with Small Parameter

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

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Veröffentlicht in:Proceedings of the National Academy of Sciences - PNAS 1984-08, Vol.81 (16), p.5267-5270
1. Verfasser: Freidlin, M. I.
Format: Artikel
Sprache:eng
Schlagworte:
Cauchy problem
Differential equations
Infinity
Mathematical functions
Mathematical manifolds
Physical Sciences: Mathematics
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Zusammenfassung:We consider two classes of quasi-linear parabolic equations depending on a small parameter ε . The asymptotic behavior of the solutions as t → ∞ and ε → 0 is investigated by studying the associated Markov family. We find its dependence on the way t and ε-1go to infinity and on the initial point.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.81.16.5267