A nonlocal parabolic problem in an annulus for the Heaviside function in Ohmic heating

In this paper, we consider the nonlocal parabolic equation ut=D u+\frac{l H(1-u)}{\big(\intAr, R H(1-u)dx\big)2}, x\in Ar, R \subset R2, t>0, with a homogeneous Dirichlet boundary condition, where l is a positive parameter, H is the Heaviside function and Ar, R is an annulus. It is shown for the radial symmetric case that: there exist two critical values l* and l*, so that for 0

Anahtar Kelimeler:

Key words: Nonlocal parabolic equation, steady state, stability, blow-up

A nonlocal parabolic problem in an annulus for the Heaviside function in Ohmic heating

Keywords:

Key words: Nonlocal parabolic equation, steady state, stability, blow-up,

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