Decay rates of energy of the 1D damped original nonlinear wave equation
For one-dimension damped original nonlinear wave equations, the author constructed a new energy functional and considered its decay rate. Specifically speaking, he proved that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This fact can be used to recover the classical exponential, polynomial, or logarithmic decay rate for the linear, polynomial or exponentially degenerating damping force near the origin, respectively.
scientific article; zbMATH DE number 7446125
scientific article