In [] Fujita showed that for positive solutions, the initial value problem (in RN) for ut= Δu+ up
with p> 1 exhibited the following behavior: If p< pc≡ 1+ 2/N, then the initial value problem …

There is an enormous amount of work in the literature about the blow-up behavior of
evolution equations. It is our intention to introduce the theory by emphasizing the methods …

In this paper we consider the wave equations with power type nonlinearities including time-
derivatives of unknown functions and their weakly coupled systems. We propose a …

This paper considers the time-weighted parabolic system ut= Δu+ eαtvp, vt= Δv+ eβtuq in
bounded domain with α, β∈ R and p, q> 0, subject to null Dirichlet boundary condition. The …

We consider two hyperbolic systems: utt= Δu+| v| p, vtt= Δv+| u| q and utt= Δu+| vt| p, vtt= Δv+|
ut| q in Rn×(0,∞) with u (x, 0)= f (x), v (x, 0)= h (x), ut (x, 0)= g (x), vt (x, 0)= k (x). We show that …

We consider the Cauchy problem for systems of semilinear wave equations in two and three
space dimensions with small initial data. Del Santo et al.[“Geometric Optics and Related …

We consider the Cauchy problem for the system of semilinear damped wave equations with
small initial data: We show that a critical exponent which classifies the global existence and …

We establish blow-up results for a system of semilinear hyperbolic inequalities in an exterior
domain of the half-space. The considered system is investigated under an inhomogeneous …

In this paper, we consider the blow-up phenomenon for the-heat equation on graph with
Dirichlet boundary conditions and a reaction term where is called the discrete weighted …

The aim of this work is twofold. One is to develop an approach for dealing with semilinear
wave equations adopted by John [38]. In Section 2, the basis of the argument will be …