The Critical Exponent to Cauchy Problem for a Time Fractional Semi-Linear Equation with a Structural Damping

Authors

Khaoula Bouguetof, Laboratory of Mathematics, Informatics and Systems, University of Larbi Tebessi, Tebessa, AlgeriaFollow

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.

Digital Object Identifier (DOI)

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

Recommended Citation

Bouguetof, Khaoula (2021) "The Critical Exponent to Cauchy Problem for a Time Fractional Semi-Linear Equation with a Structural Damping," Applied Mathematics & Information Sciences: Vol. 15: Iss. 2, Article 9.
DOI: http://dx.doi.org/10.18576/amis/150209
Available at: https://digitalcommons.aaru.edu.jo/amis/vol15/iss2/9