Asymptotics for fractional nonlinear heat equations

Nakao Hayashi, Elena I. Kaikina, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


The Cauchy problem is studied for the nonlinear equations with fractional power of the negative Laplacian {ut+(-δ)α\2 u + u1+σ = 0, u(0,x) = u0(x), x ∈ Rn, t> 0, u(0,x) = u0(x), x ∈ Rn , where α ∈ ( 0,2), with critical σ = α/n and sub-critical σ ∈ (0,α/n) powers of the nonlinearity. Let u0∈ L 1,a} ∩L∞∩ C, u0(x)≥ 0 in Rn}, θ =}∫Rnn u0( x) dx>0. The case of not small initial data is of interest. It is proved that the Cauchy problem has a unique global solution u ∈ C([0,∞); L∞∩ L1,a∩ C) and the large time asymptotics are obtained.

Original languageEnglish
Pages (from-to)663-688
Number of pages26
JournalJournal of the London Mathematical Society
Issue number3
Publication statusPublished - 2005 Dec


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