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AbstractWe consider the quasilinear wave equation utt−△ut−div(|∇u|α−2∇u)−div(|∇ut|β−2∇ut)+a|ut|m−2ut=b|u|p−2u$$u_{tt} -\triangle u_{t} -\operatorname{div}\bigl(\vert \nabla u\vert ^{\alpha-2} \nabla u\bigr) - \operatorname{div}\bigl(\vert \nabla u_{t}\vert ^{\beta-2} \nabla u_{t} \bigr) +a \vert u_{t}\vert ^{m-2} u_{t} =b|u|^{p-2} u… Click to show full abstract
AbstractWe consider the quasilinear wave equation utt−△ut−div(|∇u|α−2∇u)−div(|∇ut|β−2∇ut)+a|ut|m−2ut=b|u|p−2u$$u_{tt} -\triangle u_{t} -\operatorname{div}\bigl(\vert \nabla u\vert ^{\alpha-2} \nabla u\bigr) - \operatorname{div}\bigl(\vert \nabla u_{t}\vert ^{\beta-2} \nabla u_{t} \bigr) +a \vert u_{t}\vert ^{m-2} u_{t} =b|u|^{p-2} u $$a,b>0$a,b>0$, associated with initial and Dirichlet boundary conditions at one part and acoustic boundary conditions at another part, respectively. We prove, under suitable conditions on α, β, m, p and for negative initial energy, a global nonexistence of solutions.
Journal Title: Boundary Value Problems
Year Published: 2017
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