Turkish Journal of Mathematics
Abstract
In this paper, we consider the nonlocal parabolic equation u_t=\Delta u+\frac{\lambda H(1-u)}{\big(\int_{A_{\rho, R}} H(1-u)dx\big)^2}, x\in A_{\rho, R} \subset R^2, t>0, with a homogeneous Dirichlet boundary condition, where \lambda is a positive parameter, H is the Heaviside function and A_{\rho, R} is an annulus. It is shown for the radial symmetric case that: there exist two critical values \lambda_* and \lambda^*, so that for 0
DOI
10.3906/mat-1104-9
Keywords
Nonlocal parabolic equation, steady state, stability, blow-up
First Page
37
Last Page
49
Recommended Citation
LIANG, F, GAO, H, & BU, C (2013). A nonlocal parabolic problem in an annulus for the Heaviside function in Ohmic heating. Turkish Journal of Mathematics 37 (1): 37-49. https://doi.org/10.3906/mat-1104-9
