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Conditional stability theorem for the one dimensional Klein-Gordon equation
Demirkaya, Aslihan Stanislavova, Milena
Demirkaya, Aslihan
Stanislavova, Milena
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Abstract
The paper addresses the conditional non-linear stability of the steady state solutions of the one-dimensional Klein-Gordon equation for large time. We explicitly construct the center-stable manifold for the steady state solutions using the modulation method of Soffer and Weinstein and Strichartz type estimates. The main difficulty in the one-dimensional case is that the required decay of the Klein-Gordon semigroup does not follow from Strichartz estimates alone. We resolve this issue by proving an additional weighted decay estimate and further refinement of the function spaces, which allows us to close the argument in spaces with very little time decay.
Description
This is the published version, also available here: http://dx.doi.org/10.1063/1.3660780.
Date
2011-10-24
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American Institute of Physics
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Keywords
Manifolds, Inequalities, Eigenvalues, Real functions, Fourier Transforms
Citation
Demirkaya, Asihan & Stanslavova, Milena. "Conditional stability theorem for the one dimensional Klein-Gordon equation." J. Math. Phys. 52, 112703 (2011); http://dx.doi.org/10.1063/1.3660780.