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 : 15 | Download : 7

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we consider the nonlocal parabolic equation ut=D u+\frac{l Hinsert ignore into journalissuearticles values(1-u);}{\biginsert ignore into journalissuearticles values(\intAr, R Hinsert ignore into journalissuearticles values(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
Keywords : Key words Nonlocal parabolic equation, steady state, stability, blow up