Abstract
This work studies the blow-up result of the solution of a coupled nonlocal singular viscoelastic equation with general source and localized frictional damping terms under some suitable conditions. This work is a natural continuation of the previous recent articles by Boulaaras et al. (Appl. Anal., 2020, https://doi.org/10.1080/00036811.2020.1760250; Math. Methods Appl. Sci. 43:6140–6164, 2020; Topol. Methods Nonlinear Anal., 2020, https://doi.org/10.12775/TMNA.2020.014).
Highlights
This paper is devoted to a study of the blow-up of the following system of two singular nonlinear viscoelastic equations: ⎧ ⎪⎪⎪⎪⎪⎪⎪⎪⎨vutttt 1 xx + (xvx)x t 0 g1(t s)(xux(x, s))x ds μ(x)ut = f1(u, v), t 0g2(t (xvx(x, s))x ds μ(x)vt f2(u, v), in Q, in Q
This work studies the blow-up result of the solution of a coupled nonlocal singular viscoelastic equation with general source and localized frictional damping terms under some suitable conditions
1 Introduction This paper is devoted to a study of the blow-up of the following system of two singular nonlinear viscoelastic equations:
Summary
This work studies the blow-up result of the solution of a coupled nonlocal singular viscoelastic equation with general source and localized frictional damping terms under some suitable conditions. 1 Introduction This paper is devoted to a study of the blow-up of the following system of two singular nonlinear viscoelastic equations: The problems related with localized frictional damping have been extensively studied by many teams [5], where the authors obtained an exponential rate of decay for the solution
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