scholarly journals Local and global nonexistence of solutions to nonlinear hyperbolic inequalities

2003 ◽  
Vol 16 (4) ◽  
pp. 493-499 ◽  
Author(s):  
M. Guedda
Keyword(s):  
Global Nonexistence ◽  
Nonexistence Of Solutions

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

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Gang Li ◽  
Linghui Hong ◽  
Wenjun Liu
Keyword(s):  
Initial Data ◽  
Wave Equations ◽  
Dirichlet Boundary ◽  
High Energy ◽  
Dirichlet Boundary Conditions ◽  
Kirchhoff Type ◽  
Nonexistence Result ◽  
Global Nonexistence ◽  
Viscoelastic Wave ◽  
Nonexistence Of Solutions

We consider viscoelastic wave equations of the Kirchhoff typeutt-M(∥∇u∥22)Δu+∫0tg(t-s)Δu(s)ds+ut=|u|p-1uwith Dirichlet boundary conditions, where∥⋅∥pdenotes the norm in the Lebesgue spaceLp. Under some suitable assumptions ongand the initial data, we establish a global nonexistence result for certain solutions with arbitrarily high energy, in the sense thatlim⁡t→T*-(∥u(t)∥22+∫0t∥u(s)∥22ds)=∞for some0<T*<+∞.

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