Initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity - Yang Cao; Conghui Liu (Electronic journal of differential equations, 2018)
We consider the initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity. Constructing a family of potential wells and using the logarithmic Sobolev inequality, we establish the existence of global weak solutions. we consider two cases: global boundedness and blowing-up at infinity. Moreover, we discuss the asymptotic behavior of solutions and give some decay estimates and growth estimates.