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July/August 2019 On nonlinear damped wave equations for positive operators. I. Discrete spectrum
Michael Ruzhansky, Niyaz Tokmagambetov
Differential Integral Equations 32(7/8): 455-478 (July/August 2019).

Abstract

In this paper, we study a Cauchy problem for the nonlinear damped wave equations for a general positive operator with discrete spectrum. We derive the exponential in time decay of solutions to the linear problem with decay rate depending on the interplay between the bottom of the operator's spectrum and the mass term. Consequently, we prove global in time well-posedness results for semilinear and for more general nonlinear equations with small data. Examples are given for nonlinear damped wave equations for the harmonic oscillator, for the twisted Laplacian (Landau Hamiltonian), and for the Laplacians on compact manifolds.

Citation

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Michael Ruzhansky. Niyaz Tokmagambetov. "On nonlinear damped wave equations for positive operators. I. Discrete spectrum." Differential Integral Equations 32 (7/8) 455 - 478, July/August 2019.

Information

Published: July/August 2019
First available in Project Euclid: 2 May 2019

zbMATH: 07144914
MathSciNet: MR3945764

Subjects:

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.32 • No. 7/8 • July/August 2019
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