Blow up for non-Newtonian equations with two nonlinear sources

This paper studies the following two non-Newtonian equations with nonlinear boundary conditions. Firstly, we show that finite time blow up occurs on and get a rate an estimate for of equation $k_{t}=(\left \vert k_{x}\right ^{r-2}k_{x})_{x}$, $(x,t)\in (0,L)\times (0,T)\ $with $k_{x}(0,t)=k^{\alpha }(0,t)$, $k_{x}(L,t)=k^{\beta }(L,t)$,$\ t\in $and initial function $k\left(x,0\right) =k_{0}\left( x\right) $,$\ x\in \lbrack 0,L]\ $where $r\geq 2$, $\alpha ,\beta \ $L\ $are positive constants. Secondly, boundary, rates estimates ^{r-2}k_{x})_{x}+k^{\alpha }$, $k_{x}(0,t)=0$, $ $k\left( x,0\right) ,\beta$ $L$ are