Estimates for Solutions to Fractional Damped Wave Equations in α-modulation Spaces

Abstract

In this paper, we obtain the estimates for solutions to fractional damped wave equations in α-modulation spaces using the almost orthogonality of projections and some corresponding techniques, as well as using the Bernstein multiplier theorem to obtain estimates on kernels. As an application, we obtain quantitative eatimates for the solution to the Cauchy problem of the nonlinear damped wave equation.

Keywords

α-modulation space / damped wave equation / Bernstein multiplier theorem / nonlinear Cauchy problem / 42B15 / 42B35 / 42C15

References

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