Lyapunov functions in barriers for parabolic equations and in stability problems with respect to “white noise”
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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.
KeywordsMathematical Physic White Noise Cauchy Problem Parabolic Equation Lyapunov Function
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