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 survey paper, the author examines nonlinear Volterra integral equations of the
second kind with solutions that blow-up or quench. The focus is on analytical results …

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 …

In this paper we consider the blow-up of solutions to a weakly coupled system of semilinear
damped wave equations in the scattering case with nonlinearities of mixed type. The proof of …

In this note, we prove blow-up results for semilinear wave models with damping and mass in
the scale-invariant case and with nonlinear terms of derivative type. We consider the single …

In this paper, we consider the blow-up for solutions to a weakly coupled system of semilinear
damped wave equations of derivative type in the scattering case. The assumption on the …

Firstly, we study the equation□ u=| u| q c+|∂ u| p with small data, where qc is the critical
power of Strauss conjecture and p≥ q c. We obtain the optimal estimate of the lifespan …

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 in this article the weakly coupled system of wave equations in the scale-
invariant case and with time-derivative nonlinearities. Under the assumption of small initial …