TY - JOUR
T1 - Global solutions to quasi-linear hyperbolic systems of viscoelasticity
AU - Dharmawardane, Priyanjana M.N.
AU - Nakamura, Tohru
AU - Kawashima, Shuichi
PY - 2011/6/1
Y1 - 2011/6/1
N2 - 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.
AB - 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.
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U2 - 10.1215/21562261-121441
DO - 10.1215/21562261-121441
M3 - Article
AN - SCOPUS:79957839407
SN - 0023-608X
VL - 51
SP - 467
EP - 483
JO - Kyoto Journal of Mathematics
JF - Kyoto Journal of Mathematics
IS - 2
ER -