Global Nonexistence of Solutions for Viscoelastic Wave Equations of Kirchhoff Type with High Energy

We consider viscoelastic wave equations of the Kirchhoff type utt-M(∥∇u∥22)Δu+∫0tg(t-s)Δu(s)ds+ut=|u|p-1u with Dirichlet boundary conditions, where ∥⋅∥p denotes the norm in the Lebesgue space Lp. Under some suitable assumptions on g and the initial data, we establish a global nonexistence result for certain solutions with arbitrarily high energy, in the sense that lim⁡t→T*-(∥u(t)∥22+∫0t∥u(s)∥22ds)=∞ for some 0<T*<+∞.

Abstract licence: CC BY

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