Planar Propagating Terraces and the Asymptotic One-dimensional Symmetry of Solutions of Semilinear Parabolic Equations
نویسنده
چکیده
We consider the equation ut = ∆u + f(u) on RN . Under suitable conditions on f and the initial value u0 = u(·, 0), we show that as t→∞ the solution u(·, t) approaches a planar propagating terrace, or a stacked family of planar traveling fronts. Using this result, we show the asymptotic one-dimensional symmetry of u(·, t) as well as its quasiconvergence in Lloc(R ).
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ورودعنوان ژورنال:
- SIAM J. Math. Analysis
دوره 49 شماره
صفحات -
تاریخ انتشار 2017