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

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Varlamov V.

Studia Mathematica

2000

tom 142

nr 1

71-99

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.

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1 Studia Mathematica

1 Varlamov V.

1 2000

Wyniki wyszukiwania

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