The subject of blow-up in a finite time, or at least very rapid growth, of a solution to a partial
differential equation has been an area of intense re search activity in mathematics. Some …

In this paper, we study the global existence and the global nonexistence of doubly nonlinear
degenerate parabolic systems with nonlinear boundary conditions. We first prove a local …

A class of reaction-diffusions equations with nonlinear boundary conditions and porous
medium type of diffusion is investigated by the method of upper and lower solutions. The …

This article deals with the global solutions and blow-up problems for the convective porous
medium equationut=(um) xx+ (μ/n)(un) x, x∈(0, 1), t> 0, with the nonlinear boundary …

We continue our study of the long-time behavior of nonnegative solutions for the degenerate
parabolic equation ut=(um) xx+(ϵ/n)(un) x, 0< x< 1, t> 0, subject to nonlinear boundary …

In this paper, we establish the critical global existence exponent and the critical Fujita
exponent for the nonlinear diffusion equation [Formula: see text], in R+×(0,+∞), subject to a …

The aim of this paper is to investigate the behavior of positive solutions to the following
system of evolution p-Laplace equations coupled via nonlocal sources: with nonlinear …

This paper discusses the global existence and quenching of the solution to the Newton
filtration equation with the nonlinear boundary condition. The authors also discuss the profile …

This article deals with the existence and nonexistence of global positive solutions of the
following equations: u_t=(u^ m) _ xx+ μ\over n (u^ n) _x, &x ∈ (0, 1),\t> 0\(u^ m) _x| _ x= 0 …