Some global dynamical properties of a class of pattern formation equations.

*(English)*Zbl 0691.35019The authors consider the equations

The mathematical study of (0.1) and (0.2) and their natural generalization is achieved by conceiving them as infinite dimensional dynamical systems. In this setting they are mainly concerned with the description of the asymptotic behavior of the solutions of (0.1) and (0.2). This amounts to perform a nonlinear stability analysis, to describe the structure of the associated global attractor, to compute an upper bound for its dimension, to construct absorbing sets.

Reviewer: Y.Ebihara

##### MSC:

35B45 | A priori estimates for solutions of PDE |

35K55 | Nonlinear parabolic equations |

35K25 | Higher order parabolic equations, general |

76F99 | Turbulence |

35B35 | Stability of solutions of PDE |