We investigate a semilinear time-fractional damped wave equation in one dimension, posed bounded interval. The considered involves convection term and singular potentials on extremity of the A Dirichlet boundary condition depending time-variable is imposed. Using nonlinear capacity estimates, we establish sufficient conditions for nonexistence weak solutions to problem. In particular, when inde...

The derivative nonlinear Schrödinger ~DNLS! equation, describing propagation of circularly polarized Alfvén waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model ~equal dampings of daughter waves, three-dimensional...

Let $G$ be a compact Lie group. In this article, we investigate the Cauchy problem for nonlinear wave equation with viscoelastic damping on . More precisely, some $L^2$ -estimates solution to homogeneous damped utilizing group Fourier transform We also prove that there is no improvement of any decay rate norm $\|u(t,\,\cdot )\|_{L^2(G)}$ by further assuming $L^1(G)$ -regularity initial data. Fi...