We give a sufficient condition under which the solutions of the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential blow up. The method is a modified variational approach, in the spirit of the work by Ibrahim et al. [Anal. PDE 4 (2011), 405-460].
The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential , is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.
This paper is concerned with the initial boundary value problem for a nonlocal p-Laplacian evolution equation with critical initial energy. In the framework of the energy method, we construct an unstable set and establish its invariance. Finally, the finite time blow-up of solutions is derived by a combination of the unstable set and the concavity method.
We investigate critical exponents for blow-up of nonnegative solutions to a class of parabolic inequalities. The proofs make use of a priori estimates of solutions combined with a simple scaling argument.
The initial boundary value problem for a viscoelastic equation with nonlinear damping in a bounded domain is considered. By modifying the method, which is put forward by Li, Tasi and Vitillaro, we sententiously proved that, under certain conditions, any solution blows up in finite time. The estimates of the life-span of solutions are also given. We generalize some earlier results concerning this equation.
We establish the blow-up of solutions to the Kirchhoff equation of q-Laplacian type with a nonlinear dissipative term , x ∈ Ω, t > 0.
This paper deals with the blow-up properties of the non-Newtonian polytropic filtration equation with homogeneous Dirichlet boundary conditions. The blow-up conditions, upper and lower bounds of the blow-up time, and the blow-up rate are established by using the energy method and differential inequality techniques.