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Longtime behavior of the hyperbolic equations with an arbitrary internal damping

DSpace at IIT Bombay

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Title Longtime behavior of the hyperbolic equations with an arbitrary internal damping
 
Creator FU, XY
 
Subject POLYNOMIAL DECAY-RATE
WAVE-EQUATION
BOUNDARY STABILIZATION
EXPONENTIAL DECAY
ENERGY DECAY
SYSTEM
CONTROLLABILITY
Logarithmic stability
Hyperbolic equations
Interpolation inequality
Global Carleman estimate
Resolvent Operator
 
Description This paper is devoted to a study of the longtime behavior of the hyperbolic equations with an arbitrary internal damping, under sharp regularity assumptions that both the principal part coefficients and the boundary of the space domain (in which the system evolves) are continuously differentiable. For this purpose, we derive a new point-wise inequality for second differential operators with symmetric coefficients. Then, based on a global Carleman estimate, we establish an estimate on the underlying resolvent operator of the equation, via which, we show the logarithmic decay rate for solutions of the hyperbolic equations.
 
Publisher BIRKHAUSER VERLAG AG
 
Date 2012-06-26T05:09:20Z
2012-06-26T05:09:20Z
2011
 
Type Article
 
Identifier ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK,62(4)667-680
0044-2275
http://dx.doi.org/10.1007/s00033-010-0113-0
http://dspace.library.iitb.ac.in/jspui/handle/100/13931
 
Language English