GLOBAL BLOW-UP FOR A DEGENERATE PARABOLIC EQUATION WITH A SPACE-TIME INTEGRAL SOURCE

Youpeng Chen (P. R. China)

Received June 20, 2009

Abstract

This paper deals with the blow-up properties of positive solution to the nonlocal in space and time degenerate parabolic equation with homogeneous Dirichlet conditions and nonnegative nontrivial initial datum. The local existence and uniqueness of the classical positive solution are established. Under appropriate hypotheses, it is shown that all positive solutions blow up in finite time. It is also proved that the blow-up set is the whole domain. And these differ from the local source case and the case with only space integral source. Furthermore, the blow-up rate is precisely determined for the two special cases:      and

Keywords and phrases: degenerate parabolic equation, space-time integral source, global existence, global blow-up, asymptotic behavior.