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Spectral analysis and exponential or polynomial stability of some indefinite sign damped problems

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  • In this paper, we consider two damped wave problems for which the damping terms are allowed to change their sign. Using a careful spectral analysis, we find critical values of the damping coefficients for which the problem becomes exponentially or polynomially stable up to these critical values.
    Mathematics Subject Classification: Primary: 35L05, 35B40; Secondary: 93D20, 35P10.

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  • [1]

    A. Benaddi and B. Rao, Energy decay rate of wave equations with indefinite damping, J. Differential Equations, 161 (2000), 337-357.doi: 10.1006/jdeq.2000.3714.

    [2]

    G. Chen, S. A. Fulling, F. J. Narcowich and S. Sun, Exponential decay of energy of evolution equations with locally distributed damping, SIAM J. Appl. Math., 51 (1991), 266-301.doi: 10.1137/0151015.

    [3]

    S. Cox and E. Zuazua, The rate at which energy decays in a damped string, Partial Differential Equations, 19 (1994), 213-243.doi: 10.1080/03605309408821015.

    [4]

    P. Freitas, On some eigenvalue problems related to the wave equation with indefinite damping, J. Differential Equations, 127 (1996), 213-243.doi: 10.1006/jdeq.1996.0072.

    [5]

    P. Freitas and E. Zuazua, Stability results for the wave equation with indefinite damping, J. Differential Equations, 132 (1996), 338-352.doi: 10.1006/jdeq.1996.0183.

    [6]

    I. Gohberg and M. Krein, "Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Spaces," 18 of Translations of Mathematical Monographs, American Mathematical Society, 1969.

    [7]

    B.-Z. Guo, Riesz basis approach to the stabilization of a flexible beam with a tip mass, SIAM J. Control Optim., 39 (2001), 1736-1747.doi: 10.1137/S0363012999354880.

    [8]

    B.-Z. Guo, J.-M. Wang and S.-P. Yung, On the $C_0$-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam, Systems Control Lett., 54 (2005), 557-574.doi: 10.1016/j.sysconle.2004.10.006.

    [9]

    K. Liu, Z. Liu and B. Rao, Exponential stability of an abstract non-dissipative linear system, SIAM J. Control Optim., 40 (2001), 149-165.doi: 10.1137/S0363012999364930.

    [10]

    J. E. Muoz Rivera and R. Racke, Exponential stability for wave equations with non-dissipative damping, Nonlinear Anal., 68 (2008), 2531-2551.doi: 10.1016/j.na.2007.02.022.

    [11]

    A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," 44 of Applied Math. Sciences, Springer-Verlag, New York, 1983.doi: 10.1007/978-1-4612-5561-1.

    [12]

    A. A. Shkalikov, Boundary value problems for ordinary differential equations with a parameter in the boundary conditions, Trudy Sem. Petrovsk., 9 (1983), 190-229. Russian. English transl. in J. Soviet Math. 33 (1986), 1311-1342.

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