Critical exponents for the decay rate of solutions in a semilinear parabolic equation
In: Archive for rational mechanics and analysis, Jg. 145 (1998), Heft 4, S. 331-342
Online
academicJournal
- print, 13 ref
Zugriff:
This paper is concerned with the Cauchy problem ut = uxx - |u|p-1u u in R x (0, ∞), u(x, 0) =u0(x) in R. A solution u is said to decay fast if t1/(p-1)u → 0 as t → ∞ uniformly in R, and is said to decay slowly otherwise. For each nonnegative integer k, let Λk be the set of uniformly bounded functions on R which change sign k times, and let Pk > 1 be defined by Pk = 1 + 2/(k + 1). It is shown that any nontrivial bounded solution with u0 ∈ Λk decays slowly if 1 < p < Pk, whereas there exists a nontrivial fast decaying solution with u0 ∈ Λk if p ≥ Pk.
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Critical exponents for the decay rate of solutions in a semilinear parabolic equation
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Autor/in / Beteiligte Person: | MIZOGUCHI, N ; YANAGIDA, E |
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Zeitschrift: | Archive for rational mechanics and analysis, Jg. 145 (1998), Heft 4, S. 331-342 |
Veröffentlichung: | Berlin; Heidelberg; New York, NY: Springer, 1998 |
Medientyp: | academicJournal |
Umfang: | print, 13 ref |
ISSN: | 0003-9527 (print) |
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