A p $p$ -Laplace Equation with Logarithmic Nonlinearity at High Initial Energy Level

Lifespan of solutions to a damped plate equation with logarithmic nonlinearity

“…Theorem 4.2 implies that problem (1) may admit finite time blowup solutions at arbitrarily high initial energy level. Indeed, by applying similar argument to that of the proof of Theorem 3.13 in [9] or Proposition 3.2 in [12], one sees that for any M > 0, especially for any M > d, there exist initial data u 0 and u 1 satisfying E(0) > M as well as all the conditions in Theorem 4.2. Therefore, the blow-up result in Theorem 4.2 is usually referred to as high initial energy blow-up or supercritical initial energy blow-up.…”

“…On the other hand, evolution equations with logarithmic nonlinearity have also attracted more and more attention in recent years, due to their wide applications to quantum field theory and other applied sciences. Among the huge amount of interesting literature, we only refer the interested reader to [5,6,7,8,11,12,14,15,16,19,22], where qualitative properties of solutions to hyperbolic or parabolic equations with logarithmic nonlinearities were studied. In particular, Di et al [8] considered the following initial boundary value problem for a semilinear wave equation with strong damping and logarithmic nonlinearity…”