Asymptotic behavior of solutions to the damped quasilinear equation ∂2∂t2 u(x,t) + γ∂u∂t (x,t) − ∂∂xσ ∂u∂x (x,t)) = 0 |
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| Authors: | Frederick Bloom |
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| Institution: | 1. Department of Mathematics and Statistics, University of South Carolina, Columbia, South Carolina 29208 U.S.A.;2. School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455 U.S.A. |
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| Abstract: | Asymptotic lower bounds for the L2 norms of solutions of initial-boundary value problems associated with the equation of the title are derived for a simple case in which the equation fails to exhibit strict hyperbolicity. It is shown that in such cases it can be expected that the norm of a solution will be bounded away from zero as t → +∞ even as the damping factor γ becomes infinitely large. |
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