Solutions of Kirchhoff plate equations with internal damping and logarithmic nonlinearity

for the nonlinear initial boundary value problem of Kirchhoff equation $$ \displaylines{ u_{tt}+\Delta^2 u + M(\|\nabla u\|^2)(-\Delta u) u_{t}= \ln |u|^2,\text{ in }\Omega\times (0,T), \cr u(x,0) = u_0(x), \quad u_{t}(x,0)=u_1(x),\quad x \in \Omega, u(x,t) \frac{\partial u}{\partial \eta}(x,t)=0, \partial \Omega,\; t\geq 0, }$$ where (\Omega;\)is a bounded domain \(R^2\) with smooth \(\partial\Omega\), \(T>0\) is fixed but arbitrary real number, \(M(s)\) continuous function on \([0,+\infty)\) and \(\eta\) unit outward normal \(\partial\Omega\). Our results are obtained using Galerkin method, compactness approach, potential well corresponding to logarithmic nonlinearity, energy estimates due Nakao. For more information see https://ejde.math.txstate.edu/Volumes/2021/21/abstr.html