INSTANTANEOUS SHRINKING AND LOCALIZATON OF FUNCTIONS IN Yλ(m,p,q,N) AND THEIR APPLICATIONS
Hongjun Yuan · Chinese Annals of Mathematics Series B · 2001
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=Δum-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 solutions 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.