Bounds on the Hausdorff dimension of random attractors for infinite-dimensional random dynamical systems on fractals (Q2314773)

The authors consider stochastic partial differential equations (SPDE) of parabolic type with linear multiplicative noise and their long term behavior in the sense of random attractors. Of particular consideration is the fractal domain for the solutions of the SPDE (see [\textit{J. Kigami}, Analysis on fractals. Cambridge: Cambridge University Press (2001; Zbl 0998.28004)] for the fractal domains under consideration). This article presents the relation between the properties of these fractal domains, namely the spectral exponent of the fractal, and the Hausdorff dimension of the random attractor. The method for obtaining the upper bound on the dimension of the random attractor follows [\textit{A. Debussche}, J. Math. Pures Appl. (9) 77, No. 10, 967--988 (1998; Zbl 0919.58044)].