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The paper is concerned with the Cauchy problem for second order hyperbolic evolution equations with nonlinear source in a Hilbert space, under the effect of nonlinear time-dependent damping. With the… Click to show full abstract
The paper is concerned with the Cauchy problem for second order hyperbolic evolution equations with nonlinear source in a Hilbert space, under the effect of nonlinear time-dependent damping. With the help of the method of weighted energy integral, we obtain explicit decay rate estimates for the solutions of the equation in terms of the damping coefficient and two nonlinear exponents. Specialized to the case of linear, time-independent damping, we recover the corresponding decay rates originally obtained in [ 3 ] via a different way. Moreover, examples are given to show how to apply our abstract results to concrete problems concerning damped wave equations, integro-differential damped equations, as well as damped plate equations.
Journal Title: Evolution Equations and Control Theory
Year Published: 2020
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