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Global existence and asymptotic behavior for a fractional differential equation. (English) Zbl 1121.35020

The authors are concerned with the global existence and asymptotic behavior of solutions to an initial boundary value problem of hyperbolic type. They investigate the interaction between a polynomial source and a dissipation of fractional order.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
26A33 Fractional derivatives and integrals
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
35L99 Hyperbolic equations and hyperbolic systems
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