Global solutions to quasi-linear hyperbolic systems of viscoelasticity

Priyanjana M.N. Dharmawardane, Tohru Nakamura, Shuichi Kawashima

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In the present paper, we study a large-time behavior of solutions to a quasilinear 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.

Original languageEnglish
Pages (from-to)467-483
Number of pages17
JournalKyoto Journal of Mathematics
Volume51
Issue number2
DOIs
Publication statusPublished - Jun 1 2011

Fingerprint

Quasilinear Hyperbolic System
Viscoelasticity
Global Solution
Viscoelastic Material
Damping Term
Memory Term
Uniform Estimates
Large Time Behavior
Dissipative Systems
Second-order Systems
Energy Method
Behavior of Solutions
Hyperbolic Systems
A Priori Estimates
Sobolev Spaces
Infinity
Tend
Converge
Motion
Zero

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Global solutions to quasi-linear hyperbolic systems of viscoelasticity. / Dharmawardane, Priyanjana M.N.; Nakamura, Tohru; Kawashima, Shuichi.

In: Kyoto Journal of Mathematics, Vol. 51, No. 2, 01.06.2011, p. 467-483.

Research output: Contribution to journalArticle

Dharmawardane, Priyanjana M.N. ; Nakamura, Tohru ; Kawashima, Shuichi. / Global solutions to quasi-linear hyperbolic systems of viscoelasticity. In: Kyoto Journal of Mathematics. 2011 ; Vol. 51, No. 2. pp. 467-483.
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