1
College of Science, China University of Petroleum, Qingdao 266580, Shandong Province, P.R. China
2
College of Science, China University of PetroleumCollege of Science, China University of Petroleum, Qingdao 266580, Shandong Province, P.R. China
Abstract
In this paper, we consider singular and degenerate parabolic equations $$ u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quad v_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to null Dirichlet 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.
Liu, B., & Li, F. (2015). A note on critical point and blow-up rates for singular and degenerate parabolic equations. Bulletin of the Iranian Mathematical Society, 41(5), 1195-1205.
MLA
Liu, B., & Li, F. "A note on critical point and blow-up rates for singular and degenerate parabolic equations", Bulletin of the Iranian Mathematical Society, 41, 5, 2015, 1195-1205.
HARVARD
Liu B., Li F. (2015). 'A note on critical point and blow-up rates for singular and degenerate parabolic equations', Bulletin of the Iranian Mathematical Society, 41(5), pp. 1195-1205.
CHICAGO
B. Liu & F. Li, "A note on critical point and blow-up rates for singular and degenerate parabolic equations," Bulletin of the Iranian Mathematical Society, 41 5 (2015): 1195-1205,
VANCOUVER
Liu B., Li F. A note on critical point and blow-up rates for singular and degenerate parabolic equations. BIMS. 2015;41(5):1195-1205.
