Optimal energy decay estimates will be derived for weak solutions to the Cauchy problem in of dissipative wave equations, which have lower power nonlinearities satisfying .
"Decay estimates of solutions for dissipative wave equations in with lower power nonlinearities." J. Math. Soc. Japan 56 (2) 365 - 373, April, 2004. https://doi.org/10.2969/jmsj/1191418635