- Turkish Journal of Mathematics
- Vol: 37 Issue: 1
- A nonlocal parabolic problem in an annulus for the Heaviside function in Ohmic heating
A nonlocal parabolic problem in an annulus for the Heaviside function in Ohmic heating
Authors : Fei Liang, Hongjun Gao, Charles Bu
Pages : 37-49
Doi:10.3906/mat-1104-9
View : 8 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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 0Keywords : Key words: Nonlocal parabolic equation, steady state, stability, blow-up