Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping

Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping

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We study the Shooting Mats energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping.The damping is localized in a bounded domain and near infinity, and the principal part Drive Belt of the wave equation has a variable-coefficient.We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.