Nonlinear Heat Equation with a Fractional Laplacian in a Disk

• Autorzy: Vladimir Varlamov
• Języki publikacji: EN

Abstrakty

EN

For the nonlinear heat equation with a fractional Laplacian $u_t + (-Δ)^{α/2} u = u^2$, 1 < α ≤ 2, the first initial-boundary value problem in a disk is considered. Small initial conditions, homogeneous boundary conditions, and periodicity conditions in the angular coordinate are imposed. Existence and uniqueness of a global-in-time solution is proved, and the solution is constructed in the form of a series of eigenfunctions of the Laplace operator in the disk. First-order long-time asymptotics of the solution is obtained.

Słowa kluczowe

EN

nonlinear heat equation; long-time asymptotics; fractional Laplacian; initial-boundary value problem in a disk

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 81
• Numer: 1
• Strony: 101-122

Daty

wydano

1999

otrzymano

1998-11-06

poprawiono

1999-02-01

Twórcy

autor

Vladimir Varlamov

• Departamento de Matemáticas, Escuela Colombiana de Ingeniería, A.A. 14520, Bogotá, Colombia

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