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In this article, we study the blow-up of solutions to the nonlinear parabolic equation in divergence form, ... where Ω is a bounded convex domain in Rn (n ≥ 2) with smooth boundary Ω. By constructing suitable auxiliary functions and using a differential inequality technique, when Ω ⊂ Rn (n ≥ 2), we establish conditions for the solution blow up at a finite time, and conditions for the solution to exist for all time. Also, we find an upper bound for the blow-up time. In addition, when Ω ⊂ Rn with (n ≥ 3), we use a Sobolev inequality to obtain a lower bound for the blow-up time. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the following quasilinear reaction diffusion equations {(b(u))t = r▽·(ρ(∣▽u∣2)▽u)+c(x)f(u) in Ω × (0,t*), ∂u/∂v = 0 on ∂Ω × (0,t*) u(x,0)=u0=u0(x)≤0 inΩí Here Ω is a bounded domain in Rn (n ≤ 2) with smooth boundary ∂Ω. Weighted nonlocal source satisfies c(x)f(u(x, t)) ≥ a1 + a2 (u(x, t))p(∫Ω(u(x, t))α dx)m, where a2, p, α are some positive constants and a1,m are some nonnegative constants. We make use of a differential inequality technique and Sobolev inequality to obtain a lower bound for the blow-up time of the solution. In addition, an upper bound for the blow-up time is also derived. [ABSTRACT FROM AUTHOR]

This paper deals with the global existence and blow-up of the solution for a class of nonlinear reaction diffusion problems. The purpose of this paper is to establish conditions on the data to guarantee the blow-up of the solution at some finite time, and conditions to ensure that the solution remains global. In addition, an upper bound for the 'blow-up time', an upper estimate of the 'blow-up rate', and an upper estimate of the global solution are also specified. Finally, as applications of the obtained results, some examples are presented. [ABSTRACT FROM AUTHOR]

We study the blow-up and global solutions for a class of quasilinear parabolic problems with Robin boundary conditions. By constructing auxiliary functions and using maximum principles, the sufficient conditions for the existence of blow-up solution, an upper bound for the "blow-up time," an upper estimate of the "blow-up rate," the sufficient conditions for the existence of global solution, and an upper estimate of the global solution are specified. [ABSTRACT FROM AUTHOR]

Using the upper and lower solution techniques and Hopf's maximum principle, the sufficient conditions for the existence of blow-up positive solution and global positive solution are obtained for a class of quasilinear parabolic equations subject to Neumann boundary conditions. An upper bound for the 'blow-up time', an upper estimate of the 'blow-up rate', and an upper estimate of the global solution are also specified. [ABSTRACT FROM AUTHOR]