The blow-up rate for a degenerate parabolic equation with a non-local source

[摘要] In this paper, we establish the local existence of the solution and the finite time blow-up result for the equation upsilon(tau) = (upsilon(m))(xx) + a integral(-l)(l) upsilon(q) dx, x is an element of (-l, l), tau > 0. Moreover, it is proved that the solution has global blow-up, and there exist constants C-1', C-2' such that C-1'(T-1* - tau)(-1/(q-1)) less than or equal to max (xis an element of[-l, l]) upsilon(x, tau) less than or equal to C-2'(T1* - tau)(-1/(q-1)), where T-1* is the blow-up time. (C) 2001 Elsevier Science.

[发布日期] 2001-12-15

[关键词] degenerate parabolic equation;non-local source;blow-up set;blow-up rate