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Realization of the dynamics of ODE'S in scalar parabolic PDE'S

In: Tatra Mountains Mathematical Publications, vol. 4, no. 1
Peter Poláčik
Detaily:
Rok, strany: 1994, 179 - 185
O článku:
We consider scalar parabolic PDE's $ut=Δ u+f(x, u, \nabla u)$ on a bounded, at least two-dimensional domain. We are interested in ODE's that are realizable in PDE's of this form. We say of an ODE that it is realizable if its dynamics is equivalent to the dynamics on an invariant manifold of some PDE in the considered class. The main results state that all linear ODE's (in any dimension) are realizable, and any (nonlinear) ODE has an arbitrarily small realizable perturbation. We also state analogous results for periodically forced equations of the form $ut=Δ u+g(t, x, u)$.
Ako citovať:
ISO 690:
Poláčik, P. 1994. Realization of the dynamics of ODE'S in scalar parabolic PDE'S. In Tatra Mountains Mathematical Publications, vol. 4, no.1, pp. 179-185. 1210-3195.

APA:
Poláčik, P. (1994). Realization of the dynamics of ODE'S in scalar parabolic PDE'S. Tatra Mountains Mathematical Publications, 4(1), 179-185. 1210-3195.