In 1D, the blow-up rate of solutions to the semilinear wave equation with f(u)=|u|^{p-1}u log^a(2+u^2) equals the ODE blow-up rate.
Hamza, The blow-up rate for strongly perturbed semilinear wave equ ations in the conformal regime without a radial assumption , Asymptotic Analysis, 97, no
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The blow-up rate for a non-scaling invariant semilinear wave equations
In 1D, the blow-up rate of solutions to the semilinear wave equation with f(u)=|u|^{p-1}u log^a(2+u^2) equals the ODE blow-up rate.