Abstract
This paper is concerned with the blow-up of certain solutions with positive initial energy to the following quasilinear wave equation: u t t − M N u t Δ p · u + g u t = f u . This work generalizes the blow-up result of solutions with negative initial energy.
Highlights
Let Ω be an open bounded Lipschitz domain in Rnðn ≥ 1Þ,T > 0, QT = Ω × ð0, TÞ
This paper is concerned with the blow-up of certain solutions with positive initial energy to the following quasilinear wave equation: utt − MðN uðtÞÞΔpð·Þu + gðutÞ = f ðuÞ
We have looked at the asymptotic behavior of the Kirchhoff wave equation problems
Summary
The parameters L, h, E, ρ, and P0 represent, respectively, the length of the string, the area of the cross-section, Young’s modulus of the material, the mass density, and the initial tension This equation is an extension of the classic d’Alembert’s wave equation by looking at the effects of changes in the length of the string during the vibrations. Hyperbolic problems with a constant exponent have been studied by many authors; we refer to interesting works [5–. In this work, we consider problem (1), which is more interesting and applicable in the real approach of sciences, so a finite-time blow-up for certain solutions with positive and negative initial energy has been proved.
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