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}\lef...

We investigate the conditions under which the solution of the initial-boundary value problem of the non-local equation ut = u + λ f (u)/( ∫ Ω f (u) dx) p , where Ω is a bounded domain of RN and f (u) is a positive, increasing, convex function, performs blow-up. c © 2005 Elsevier Ltd. All rights reserved.

We prove here the existence of boundary blow up solutions for fully nonlinear equations in general domains, for a nonlinearity satisfying KellerOsserman type condition. If moreover the nonlinearity is non decreasing , we prove uniqueness for boundary blow up solutions on balls for operators related to Pucci’s operators.

In this paper we consider a kind of higher-order evolution equation as^{kt^{k} + ^{k&minus1}u/t^{k&minus1} +• • •+ut &minus{delta}u= f (u, {delta}u,x). For this equation, we investigate nonglobal solution, blow-up in finite time and instantaneous blow-up under some assumption on k, f and initial data. In this paper we employ the Test function method, the eneralized convexity method an...