Initial Boundary Value Problem Of A Class Of Pseudo-parabolic Kirchhoff Equations With Logarithmic Nonlinearity

In this paper,we consider the initial boundary value problem of a class of pseudo-parabolic Kirchhoff equations with logarithmic nonlinearity.Due to the invalidation of the logarithmic Sobolev inequality,we introduce the Gagliardo-Nirenberg inequality and the interpolation inequality for L^P-norms.We use the potential well method to prove the existence and blow-up of the solution of the equation under different initial conditions.The content are summarized as follows:1.When the initial energy is J(u₀)?d,the global existence and the finite-time blow-up of the weak solution are verified.We also get the exponential decay estimate of the global solution and life span of the blow-up solution.2.When the initial energy J(u₀)>d,we find another criterion for the vanishing solution and blow-up solution.At the same time,we study the corresponding ground state solution and establish a relationship between the global solution and the ground state solution.