Global existence and blow-up of solutions for a class of Kirchhoff equations with damping terms and logarithmic nonlinearity
摘要
In this paper, a class of Kirchhoff equations with damping terms and logarithmic nonlinearity homogeneous Dirichlet boundary condition are studied. First of all, the local existence and uniqueness of weak solutions are proved by fixed point theorem. Second, we prove the global existence and decay of weak solutions at the critical and the subcritical energy levels. Finally, by applying differential inequality techniques, the blow-up result of weak solutions have been proved on low initial energy; and under high initial energy condition, we discussed the blow-up condition of weak solution.