Spectral criterion of stochastic stability for invariant manifolds 1

The mean square stability for invariant manifolds of nonlinear stochastic differential equations is considered. The stochastic stability analysis is reduced to the estimation of the spectral radius of some positive operator. For the important case of manifolds with codimension one, a constructive spectral analysis of this operator is carried out. On the basis of this spectral technique, parametrical criteria of the stochastic stability of limit cycle and 2-torus are developed. © 2013 Springer Science+Business Media New York

Dirichlet boundary conditions for degenerate and singular nonlinear parabolic equations

We study existence and uniqueness of solutions to a class of quasilinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To this purpose some barrier functions are properly introduced and used