Behavior of Solutions to a Coupled Kirchhoff-Type Parabolic System With Singular Potential and Logarithmic Nonlinearity

In this paper, we apply the modified potential well method and the variational method to study the long-time behaviors of solutions to a coupled Kirchhoff-type parabolic system with singular potential and logarithmic nonlinearity. By classifying the initial energy (J(u₀, v₀) < d, = d, > d), we obtain global existence and finite-time blow-up of solutions. Noting that the value of the potential well depth d is very small such that it is difficult to calculate precisely, by the concavity method, we also discuss finite time blow-up of solutions independent of d. Furthermore, we derive new threshold criteria for extinction and non-extinction phenomena of solutions, and obtain the threshold time for the extinction phenomenon under some appropriate conditions.