Open Access
Summer 2011 Global solutions to quasi-linear hyperbolic systems of viscoelasticity
Priyanjana M. N. Dharmawardane, Tohru Nakamura, Shuichi Kawashima
Kyoto J. Math. 51(2): 467-483 (Summer 2011). DOI: 10.1215/21562261-1214411


In the present paper, we study a large-time behavior of solutions to a quasi-linear second-order hyperbolic system which describes a motion of viscoelastic materials. The system has dissipative properties consisting of a memory term and a damping term. It is proved that the solution exists globally in time in the Sobolev space, provided that the initial data are sufficiently small. Moreover, we show that the solution converges to zero as time tends to infinity. The crucial point of the proof is to derive uniform a priori estimates of solutions by using an energy method.


Download Citation

Priyanjana M. N. Dharmawardane. Tohru Nakamura. Shuichi Kawashima. "Global solutions to quasi-linear hyperbolic systems of viscoelasticity." Kyoto J. Math. 51 (2) 467 - 483, Summer 2011.


Published: Summer 2011
First available in Project Euclid: 22 April 2011

zbMATH: 1228.35136
MathSciNet: MR2793275
Digital Object Identifier: 10.1215/21562261-1214411

Primary: 35B40 , 35L51 , 74D10

Rights: Copyright © 2011 Kyoto University

Vol.51 • No. 2 • Summer 2011
Back to Top