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

Authors

FEI LIANG
HONGJUN GAO
CHARLES BU

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, FEI; GAO, HONGJUN; and BU, CHARLES (2013) "A nonlocal parabolic problem in an annulus for the Heaviside function in Ohmic heating," Turkish Journal of Mathematics: Vol. 37: No. 1, Article 5. https://doi.org/10.3906/mat-1104-9
Available at: https://journals.tubitak.gov.tr/math/vol37/iss1/5