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Longterm dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent
1.  Department of Mechanics and Mathematics, Kharkov National University, Kharkov, 61077 
2.  Department of Mathematics, University of Virginia, Charlottesville, VA 22903 
3.  Department of Mathematics, University of NebraskaLincoln, Lincoln, NE 68588, United States 
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Aníbal RodríguezBernal, Enrique Zuazua. Parabolic singular limit of a wave equation with localized boundary damping. Discrete & Continuous Dynamical Systems  A, 1995, 1 (3) : 303346. doi: 10.3934/dcds.1995.1.303 
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