TY - JOUR
AU - Abita, Rahmoune
PY - 2022/12/04
Y2 - 2024/02/26
TI - Bounds for blow-up solutions of a semilinear pseudo-parabolic equation with a memory term and logarithmic nonlinearity in variable space
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 128
IS - 3
SE - Articles
DO - 10.7146/math.scand.a-133418
UR - https://www.mscand.dk/article/view/133418
SP -
AB - <p>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 \[ u_{t}-\Delta u_{t}+\int _{0}^{t}g( t-s) \Delta u( x,s) \mathrm {d}s-\Delta u\]\[=|u|^{p(\cdot ) -2}u\ln (|u|), \]with a Dirichlet boundary condition.</p><p>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.</p>
ER -