INSTANTANEOUS SHRINKING AND LOCALIZATION OF FUNCTIONS IN Y_λ(m,p,q,N) AND THEIR APPLICATIONS

The aim of this paper is to discuss the instantaneous shrinking and localization of the support of functions in Yλ(m,p,q,N) and their applications to some nonlinear parabolic equations including the porous medium equation ut = △um-uq, m > 0, q > 0 and the p-Laplace equation ut = div(|△u|p-2△u)-uq, P > 1, q > 0. In particular, as an application of the results, the necessary and sufficient condition for the solutious of the above p-Laplace equation with nonnegative finite Borel measures as initial conditions to have the instantaneous shrinking property of the support is obtained. This is an answer to an open problem posed by R. Kersner and A. Shishkov.