A permutation characterization of Sturm global attractors of Hamiltonian type

作者：Fiedler Bernold; Rocha Carlos^*; Wolfrum Matthias

来源：Journal of Differential Equations, 2012, 252(1): 588-623.

DOI：10.1016/j.jde.2011.08.013

We consider Neumann boundary value problems of the form u(t) = u(xx) + f on the interval 0 %26lt;= x %26lt;= pi for dissipative nonlinearities f = f (u). A permutation characterization for the global attractors of the semiflows generated by these equations is well known, even in the much more general case f = f (x, u, u(x)) We present a permutation characterization for the global attractors in the restrictive class of nonlinearities f = f (u). In this class the stationary solutions of the parabolic equation satisfy the second order ODE v %26apos;%26apos;+ f (v) = 0 and we obtain the permutation characterization from a characterization of the set of 2 pi-periodic orbits of this planar Hamiltonian system. Our results are based on a diligent discussion of this mere pendulum equation.

• 出版日期2012-1-1