Blow Up in a Nonlinearly Damped Wave Equation

Blow up in the Cauchy problem for a nonlinearly damped wave equation

In this paper we consider the Cauchy problem for the nonlinearly damped wave equation with nonlinear source utt −∆u + aut|ut|m−2 = bu|u|p−2, p > m. We prove that given any time T > 0, there exist always initial data with sufficiently negative initial energy, for which the solution blows up in time ≤ T. This result improves an earlier one by Todorova [11].

Existence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.

Exponential decay of solutions of a nonlinearly damped wave equation

The issue of stablity of solutions to nonlinear wave equations has been addressed by many authors. So many results concerning energy decay have been established. Here in this paper we consider the following nonlinearly damped wave equation utt −∆u+ a(1 + |ut|)ut = bu|u|p−2, a, b > 0, in a bounded domain and show that, for suitably chosen initial data, the energy of the solution decays exponenti...

Global Nonexistence in a Nonlinearly Damped Wave Equation

Instability of Standing Waves of the Schrödinger Equation with Inhomogeneous Nonlinearity

This paper is concerned with the inhomogeneous nonlinear Shrödinger equation (INLS-equation) iut +∆u+ V ( x)|u|u = 0, x ∈ R . In the critical and supercritical cases p ≥ 4/N, with N ≥ 2, it is shown here that standing-wave solutions of (INLS-equation) on H1(RN ) perturbation are nonlinearly unstable or unstable by blow-up under certain conditions on the potential term V with a small > 0.