| Abstract: |
| In this talk, we are concerning the asymptotic behavior of noncompact orbits for dynamical systems. First we introduce a semilinear parabolic problem defined onentire spatial domain as a typical example and give a typical behavior which comes from the noncompactness of the spatial domain. The possibility to develop a general dynamical system theory allowing the noncompactness of the orbit (i.e., a generalization of the LaSalle principle) will be also discussed. The method is based on the profile decomposition. |
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