Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity

Bounds for lifespan of solutions to strongly damped semilinear wave equations with logarithmic sources and arbitrary initial energy

“…Finally, a lower bound for blow-up time is obtained by introducing a new control functional. These results fill the gap of [5].…”

“…

The main aim of this paper is to deal with the upper and lower bounds for blow-up time of solutions to the following equation:which has been studied in [5]. For high initial energy, it is well known that the classical potential well method is not effective.

…”

“…which has been studied in [5]. For high initial energy, it is well known that the classical potential well method is not effective.…”

“…with p > 1 and a ∈ R. They showed that exact blow-up rate of any singular solution in the one space dimensional case. In 2019, Di, Shang and Song in [5] discussed the existence, uniqueness of global weak solutions to Problem (1) and obtained the finite time blow-up results of weak solutions under some appropriate conditions. However, there exist some unsolved problems in their paper.…”

“…• In [5], the authors proved that the solution blew up in finite time for 2 < p < 2 * and gave an estimate of the lower bound for blow-up time when 2 < p < 1 + n n−2 . Naturally, when 1 + n n−2 < p < 2n n−2 , whether is a similar result obtained?…”