On energy decay-nondecay problems for wave equations with nonlinear dissipative term in \(\mathbb{R}^ N\) (Q1898876)

For the Cauchy problem associated with the wave equation with nonlinear dissipative term \(w_{tt}- \Delta w+ \lambda w+ \beta(x, t, w_t) w_t= 0\), \((x, t)\in \mathbb{R}^N\times (0, \infty)\), the authors study the decay and nondecay of energy for certain types of nonlinearity. Their results generalize some previous ones of Mochizuki, Nakao and Motai. The main tool in the proofs is a weighted energy estimate.