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Decay rates for second order evolution equations in Hilbert spaces with nonlinear time-dependent damping

  • Corresponding author: Ti-Jun Xiao

    Corresponding author: Ti-Jun Xiao

The work was supported partly by the NSF of China (11771091, 11831011), the Fudan University (IDH 1411016), and the Shanghai Key Laboratory for Contemporary Applied Mathematics (08DZ2271900)

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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 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.

    Mathematics Subject Classification: 35B40, 35L70, 35L90.

    Citation:

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