Seminar on PDE
主講者: Prof. Eiji Yanagida (Department of Mathematics, Tokyo Institute of Technology)
講題: Existence of non-stabilizing solutions of a semilinear parabolic equation
時間: 2014-04-23 (Wed.)  10:30 - 11:30
地點: 數學所 617 研討室 (台大院區)
Abstract: We examine the behavior of positive localized solutions of semilinear parabolic equations. In all previously known examples, bounded localized solutions are convergent or at least quasiconvergent in the sense that all their limit profiles are steady states. In this talk, it is shown that such a general conclusion is not valid in three or higher dimensional case even if the solutions in question are radially symmetric. Specifically, we give examples of positive bounded localized solutions whose limit set is infinite and contains only one equilibrium. This is a joint work with Peter Polacik.
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