Preprint of the project: SFB 701: Spectral Structures and Topological Methods in Mathematics  Project B3Numerical Analysis of equivariant evolution equations12139 Denny Otten. In this paper we study solutions of nonlinear systems \[A\Delta v (x) + \langle Sx, \nabla v(x)\rangle + f (v(x)) = 0,\quad x \in \mathbb{R}^d,\; d\geq 2.\] The linear operator is of OrnsteinUhlenbeck type with an unbounded drift term defined by a skewsymmetric matrix \(S\in\mathbb{R}^{d,d}.\) Equations of this form determine the shape and angular speed of rotating waves in timedependent reaction diffusion systems. We prove under certain conditions that every classical solution which falls below a certain threshold at infinity, must decay exponentially in space. For the proof we utilize the heat kernel matrix of a generalized OrnsteinUhlenbeck operator, determine its maximal domain and analyze constant and variable coefficient perturbations.
