scholarly journals Exact controllability of the wave equation with Neumann boundary condition and time-dependent coefficients

1999 ◽  
Vol 8 (1) ◽  
pp. 53-89 ◽  
Author(s):  
Marcelo Moreira Cavalcanti
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Neumann Boundary Condition ◽  
Exact Controllability ◽  
Neumann Boundary ◽  
Time Dependent

scholarly journals Blow-up for the wave equation with nonlinear source and boundary damping terms

2015 ◽  
Vol 145 (4) ◽  
pp. 759-778 ◽  
Author(s):  
Alessio Fiscella ◽  
Enzo Vitillaro
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Initial Data ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Neumann Boundary ◽  
Nonlinear Dissipation ◽  
Typical Problem ◽  
Nonlinear Source ◽  
Boundary Damping

The paper deals with blow-up for the solutions of an evolution problem consisting in a semilinear wave equation posed in a boundedC1,1open subset of ℝn, supplied with a Neumann boundary condition involving a nonlinear dissipation. The typical problem studied iswhere∂Ω=Γ0∪Γ1,Γ0∩Γ1= ∅,σ(Γ0) > 0, 2 <p≤ 2(n− 1)/(n− 2) (whenn≥ 3),m> 1,α∈L∞(Γ1),α≥ 0 andβ≥ 0. The initial data are posed in the energy space.The aim of the paper is to improve previous blow-up results concerning the problem.

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