Abstract
AbstractOf concern is the energy decay property of solutions to wave equations with time-dependent damping. A reasonable class of damping coefficients for the framework of weighted energy methods is proposed, which contains not only the model of “effective” damping$$(1+t)^{-\beta }$$(1+t)-β$$(-1\le \beta <1)$$(-1≤β<1), but also non-differentiable functions with a suitable behavior at$$t\rightarrow \infty $$t→∞. As an application of the weighted energy estimate, global existence for the corresponding semilinear wave equation is discussed.
Funder
Tokyo University of Science
Publisher
Springer Science and Business Media LLC
Subject
Mathematics (miscellaneous)
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