Abstract
Sufficient conditions for the existence of an inertial manifold for the equation \(u_{tt}-2\gamma _{s} \varDelta u_t +2\gamma _{w} u_t - \varDelta u = f(u)\), \(\gamma _{s} > 0\), \(\gamma _{w} \ge 0\) are found. The nonlinear function \(f\) is supposed to satisfy Lipschitz property. The proof is based on construction of a new inner product in the phase space in which the conditions of a general theorem on the existence of inertial manifolds for an abstract differential equation in a Hilbert space are satisfied.
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References
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Acknowledgments
The author express her gratitude to A. Yu. Goritsky and V. V. Chepyzhov for setting the problem and permanent attention to the research.
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Chalkina, N. (2014). Inertial Manifolds and Spectral Gap Properties for Wave Equations with Weak and Strong Dissipation. In: Zgurovsky, M., Sadovnichiy, V. (eds) Continuous and Distributed Systems. Solid Mechanics and Its Applications, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-319-03146-0_14
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DOI: https://doi.org/10.1007/978-3-319-03146-0_14
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