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

Studia Mathematica (2000)

- Volume: 142, Issue: 1, page 71-99
- ISSN: 0039-3223

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topVarlamov, Vladimir. "Long-time asymptotics for the nonlinear heat equation with a fractional Laplacian in a ball." Studia Mathematica 142.1 (2000): 71-99. <http://eudml.org/doc/216790>.

@article{Varlamov2000,

abstract = {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.},

author = {Varlamov, Vladimir},

journal = {Studia Mathematica},

keywords = {first initial-boundary value problem; nonlinear heat equation; construction of solutions; higher-order long-time asymptotics; fractional Laplacian; long time asymptotics},

language = {eng},

number = {1},

pages = {71-99},

title = {Long-time asymptotics for the nonlinear heat equation with a fractional Laplacian in a ball},

url = {http://eudml.org/doc/216790},

volume = {142},

year = {2000},

}

TY - JOUR

AU - Varlamov, Vladimir

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

JO - Studia Mathematica

PY - 2000

VL - 142

IS - 1

SP - 71

EP - 99

AB - 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.

LA - eng

KW - first initial-boundary value problem; nonlinear heat equation; construction of solutions; higher-order long-time asymptotics; fractional Laplacian; long time asymptotics

UR - http://eudml.org/doc/216790

ER -

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