TY - JOUR
T1 - NON-EXISTENCE OF GLOBAL WEAK SOLUTIONS TO SEMI-LINEAR WAVE EQUATIONS INVOLVING TIME-DEPENDENT STRUCTURAL DAMPING TERMS
AU - Kirane, M.
AU - Fino, A. Z.
AU - Kerbal, S.
AU - Laadhari, A.
N1 - Publisher Copyright:
© 2024, Institute of Applied Mathematics of Baku State University. All rights reserved.
PY - 2024
Y1 - 2024
N2 - We consider a semilinear wave equation involving a time-dependent structural damping term of the form1 (Formula presented). Our results show the influence of the parameters β, σ on the nonexistence of global weak solutions under assumptions on the given system data. Our approach is based on the nonlinear capacity method combined with a pointwise estimate of the fractional Laplacian of some test functions, which was derived by Fujiwara (2018) (see also Fino and Dao (2022)). We extend the blowu-p results developed recently by Fino and Hamza (2022).
AB - We consider a semilinear wave equation involving a time-dependent structural damping term of the form1 (Formula presented). Our results show the influence of the parameters β, σ on the nonexistence of global weak solutions under assumptions on the given system data. Our approach is based on the nonlinear capacity method combined with a pointwise estimate of the fractional Laplacian of some test functions, which was derived by Fujiwara (2018) (see also Fino and Dao (2022)). We extend the blowu-p results developed recently by Fino and Hamza (2022).
KW - Blow-Up
KW - Damped Wave Equations
KW - Fractional Laplacian
KW - Variable Coefficients
UR - http://www.scopus.com/inward/record.url?scp=85190982587&partnerID=8YFLogxK
U2 - 10.30546/1683-6154.23.1.2024.110
DO - 10.30546/1683-6154.23.1.2024.110
M3 - Article
AN - SCOPUS:85190982587
SN - 1683-3511
VL - 23
SP - 110
EP - 129
JO - Applied and Computational Mathematics
JF - Applied and Computational Mathematics
IS - 1
ER -