Well-posedness and linearization for a semilinear wave equation with spatially growing nonlinearity

We investigate the initial value problem for a defocusing semi-linear wave equation with spatially growing nonlinearity. Our analysis leads to global well-posedness in the energy space. Furthermore, we obtain the linearization of energy-bounded solutions using the methodology outlined in [8]. The proof hinges on Moser-Trudinger type inequalities and Strichartz estimates.
Comment: Typos corrected and text revised