Russian Journal of Mathematical Physics

, Volume 21, Issue 4, pp 472–483 | Cite as

Lyapunov functions in barriers for parabolic equations and in stability problems with respect to “white noise”

  • L. A. KalyakinEmail author


The Cauchy problem for a parabolic equation with a small parameter multiplying the highest derivatives is considered. The dynamical system corresponding to the limit equation of the first order has an asymptotically stable equilibrium. A Lyapunov function known in a neighborhood of this equilibrium is used to construct a barrier in the Cauchy problem for the original parabolic equation. This result is applied to study the dynamical system with respect to random perturbations of the “white noise” type.


Mathematical Physic White Noise Cauchy Problem Parabolic Equation Lyapunov Function 
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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Institute of Mathematics with Computing Centre, Ufa Science CentreRussian Academy of SciencesUfaRussia

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