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Author Country (or Countries)

Algeria

Abstract

In this paper, we study the semilinear equation with a time fractional structural damping Dβ0|tu(t,x)−2∆Dα0|tu(t,x)+∆2u(t,x) = |u(t,x)|p t > 0, x ∈ Ω, where p > 1, 1 < α < 1 < β < 2 and Dα is the Caputo fractional derivative. We obtain the blow- up result under some positive data 2 0|t when 1 < p < 1+ 2α . Whereas, if p 􏰁 1+ 2α and ∥u0∥L2qc (Ω), qc = N(p−1)/4 is sufficiently small, we prove the existence of global solution.

Suggested Reviewers

N/A

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/150209

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