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2000 | 142 | 1 | 71-99
Tytuł artykułu

Long-time asymptotics for the nonlinear heat equation with a fractional Laplacian in a ball

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The nonlinear heat equation with a fractional Laplacian $[u_t+(-Δ)^{α/2} u = u^2, 0 < α ≤ 2]$, is considered in a unit ball $B$. Homogeneous boundary conditions and small initial conditions are examined. For 3/2 + ε₁ ≤ α ≤ 2, where ε₁ > 0 is small, the global-in-time mild solution from the space $C⁰([0,∞), H₀^{κ}(B))$ with κ < α - 1/2 is constructed in the form of an eigenfunction expansion series. The uniqueness is proved for 0 < κ < α - 1/2, and the higher-order long-time asymptotics is calculated.
Czasopismo
Rocznik
Tom
142
Numer
1
Strony
71-99
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-11-02
poprawiono
2000-03-06
Twórcy
  • Department of Mathematics, The University of Texas at Austin, Austin, TX 78712-1082, U.S.A.
Bibliografia
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Bibliografia
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