Geodesic
Long-time asymptotics for the nonlinear heat equation with a fractional Laplacian in a ball
Studia Mathematica, Tome 142 (2000) no. 1, pp. 71-99 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm-142-1-71-99
Keywords: first initial-boundary value problem, nonlinear heat equation, construction of solutions, higher-order long-time asymptotics, fractional Laplacian 
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     title = {Long-time asymptotics for the nonlinear heat equation with a fractional {Laplacian} in a ball},
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Vladimir Varlamov. Long-time asymptotics for the nonlinear heat equation with a fractional Laplacian in a ball. Studia Mathematica, Tome 142 (2000) no. 1, pp. 71-99. doi: 10.4064/sm-142-1-71-99

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