Structural stability for time-periodic one-dimensional parabolic equations (Q1188254)

The authors study an infinite-dimensional dynamical system generated by a time-periodic one-dimensional semilinear scalar parabolic equation \[ u_ t=u_{xx}+ f(t,x,u),\;t>0,\;0<x<L, \qquad u(t,0)=u(t,L)=0,\;t>0, \tag{1} \] with the initial data \(u(0,x)_ =u_ 0(x)\), \(0\leq x\leq L\). Under suitable conditions, they associate a framework of dynamical systems to the foregoing problem in terms of the Poincaré map \(\Pi\) and then define the iteration \(\Pi^ n\). The aim of the paper is to study global dynamical aspects of the semiflow \(\{\Pi^ n\}_{n\geq 0}\).