BOUNDS FOR BLOW-UP SOLUTIONS OF A SEMILINEAR PSEUDO-PARABOLIC EQUATION WITH A MEMORY TERM AND LOGARITHMIC NONLINEARITY IN VARIABLE SPACE

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 ut(1) - Delta ut + integral(t)(0) g(t - s)Delta u(x, s) ds - Delta u = |u|p(center dot)-2 u ln(|u|), with a Dirichlet boundary condition. Under appropriate assumptions about the relaxation function g, the initial data u0 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.