Journals / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 1
A nonlocal parabolic problem in an annulus for the Heaviside function in Ohmic heating
- Pages
- 37–49
- DOI
- —
Abstract
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
Özet
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