- Tytuł:
- Long-time asymptotics for the nonlinear heat equation with a fractional Laplacian in a ball
- Autorzy:
- Varlamov, Vladimir
- Powiązania:
- https://bibliotekanauki.pl/articles/1206006.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
first initial-boundary value problem
nonlinear heat equation
construction of solutions
higher-order long-time asymptotics
fractional Laplacian - Opis:
- 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.
- Źródło:
-
Studia Mathematica; 2000, 142, 1; 71-99
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł