Blow up and Decay estimates for a certain type of logarithmic Klein-Gordon equations

In this project, we consider the issue of blow up and the decay estimates of solutions for certain initial boundary value problems for the logarithmic Klein-Gordon equation in regular bounded domains. This type of problems is encountered in many branches of physics such as Nuclear Physics, Optics and Geophysics. It is well known, from the Quantum Field Theory, that such kind of logarithmic nonlinearity appears naturally in inflation Cosmology and in Supersymmetric field theories. Our aim here is to discuss the blow up of solutions for certain problems related to the nonlinear Klein-Gordon equation where the source term is nonlinear and of logarithmic type. In addition, we intend to study the effect of the viscoelastic damping on the stability and/or the blow up in the presence/absence of the viscoelasticity. Finally, it is of much importance to see also the effect of the time delay to the above-mentioned results. Constructing appropriate Lyapunov functional together with the multiplier method or the energy methods are powerful tools to reach our goals.