%0 Journal Article
%T A note on critical point and blow-up rates for singular and degenerate parabolic equations
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Liu, B.
%A Li, F.
%D 2015
%\ 10/01/2015
%V 41
%N 5
%P 1195-1205
%! A note on critical point and blow-up rates for singular and degenerate parabolic equations
%K singular and degenerate parabolic equations
%K blow-up classification
%K simultaneous blow-up rates
%R
%X In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determined. Additionally, we obtain blow-up rates and sets for the solutions. The singular rates for the derivation of the solutions are given.
%U http://bims.iranjournals.ir/article_684_61771b8a5c6442802437ee788e2c3fce.pdf