EXPONENTIAL STABILITY TO A QUASILINEAR
HYPERBOLIC EQUATION WITH INTERNAL DAMPING
Ducival C. Pereira1, Celsa H.M. Maranhão2,
José A.D. Chuquipoma3, Carlos A. Raposo4
1 Department of Mathematics
State University of Pará
Pará, 66113-200, BRAZIL
2Department of Mathematics
Federal University of Pará
Pará, 66075-110, BRAZIL
3,4Department of Mathematics
Federal University of São João del-Rey
São João del-Rey, 36307-352, BRAZIL
Abstract. In this work we prove that the effect of the memory together with the frictional damping produces stabilization for the system of two identical laminated beams of uniform density taking into account that an adhesive of small thickness is bonding the two beams and produce the interfacial slip. It is assumed that the thickness of the adhesive is small enough so that the contribution of its mass to the kinetic energy of the entire beam may be ignored.
AMS Subject Classification: 35B40, 35L72, 35B35
Key Words and Phrases: exponential stability, quasilinear hyperbolic equation, energy method


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DOI: 10.12732/ijam.v29i3.9

Volume: 29
Issue: 3
Year: 2016