Bounds for blow-up solutions of a semilinear pseudo-parabolic equation with a memory term and logarithmic nonlinearity in variable space - Abita, Rahmoune (MATHEMATICA SCANDINAVICA, 2022)
In this article, we investigate the initial boundary value problem for a pseudo-parabolic equation under the influence of a linear memory term and a logarithmic nonlinear source term \[ u_t-Δ u_t+_0^tg( t-s) Δ u( x,s) ds-Δ u\]\[=|u|^p(· ) -2u(|u|), \]with a Dirichlet boundary condition. Under appropriate assumptions about the relaxation function g, the initial data u_0 and the function exponent p, we not only set the lower bounds for the blow-up time of the solution when blow-up occurs, but also by assuming that the initial energy is negative, we give a new blow-up criterion and an upper bound for the blow-up time of the solution.