Author/Authors :
Liu، Bingchen نويسنده College of Science, China University of Petroleum , , Li، Fengjie نويسنده College of Science, China University of Petroleum ,
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 $m,n, p,q\ge 0$, $\alpha, \beta\in [0,2)$ and $x_0\in (0,a)$. 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.
