TY - JOUR ID - 684 TI - A note on critical point and blow-up rates for singular and degenerate parabolic equations JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Liu, B. AU - Li, F. AD - College of Science‎, ‎China University of Petroleum‎, ‎Qingdao 266580‎, ‎Shandong Province‎, ‎P.R‎. ‎China AD - College of Science, China University of PetroleumCollege of Science‎, ‎China University of Petroleum‎, ‎Qingdao 266580‎, ‎Shandong Province‎, ‎P.R‎. ‎China Y1 - 2015 PY - 2015 VL - 41 IS - 5 SP - 1195 EP - 1205 KW - singular and degenerate parabolic equations‎ KW - ‎blow-up classification‎ KW - ‎simultaneous blow-up rates‎ DO - N2 - 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. UR - http://bims.iranjournals.ir/article_684.html L1 - http://bims.iranjournals.ir/article_684_61771b8a5c6442802437ee788e2c3fce.pdf ER -