For the strongly damped semilinear wave equation with initial data scaled by amplitude ρ, solutions exist for a time interval at least of length comparable to ρ^{-(p-2)}.
Alabau-Boussouira, Appl
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Lifespan Lower Estimates for a Strongly Damped Semilinear Wave Equation
For the strongly damped semilinear wave equation with initial data scaled by amplitude ρ, solutions exist for a time interval at least of length comparable to ρ^{-(p-2)}.