Abstract
In this paper, we shall discuss the stability of smooth monotone travelling wave solutions for viscoelastic materials with memory. It is known that a smooth monotone travelling wave solution exists for (1.1) if the end states are close and satisfy the Rankine-Hugoniot condition. For such a travelling wave, we shall show that if the initial data are close to a travelling wave solution, the solutions to (1.1) will approach the travelling wave solution in sup norm as the time goes to infinity. For the constitutive relations, we shall discuss two cases: convex and nonconvex.
| Original language | English |
|---|---|
| Pages (from-to) | 174-196 |
| Number of pages | 23 |
| Journal | Journal of Differential Equations |
| Volume | 127 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1996 May 1 |
| Externally published | Yes |
Fingerprint
ASJC Scopus subject areas
- Analysis
Cite this
Nonlinear stability of travelling wave solutions for viscoelastic materials with fading memory. / Hattori, Harumi; Kawashima, Shuichi.
In: Journal of Differential Equations, Vol. 127, No. 1, 01.05.1996, p. 174-196.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Nonlinear stability of travelling wave solutions for viscoelastic materials with fading memory
AU - Hattori, Harumi
AU - Kawashima, Shuichi
PY - 1996/5/1
Y1 - 1996/5/1
N2 - In this paper, we shall discuss the stability of smooth monotone travelling wave solutions for viscoelastic materials with memory. It is known that a smooth monotone travelling wave solution exists for (1.1) if the end states are close and satisfy the Rankine-Hugoniot condition. For such a travelling wave, we shall show that if the initial data are close to a travelling wave solution, the solutions to (1.1) will approach the travelling wave solution in sup norm as the time goes to infinity. For the constitutive relations, we shall discuss two cases: convex and nonconvex.
AB - In this paper, we shall discuss the stability of smooth monotone travelling wave solutions for viscoelastic materials with memory. It is known that a smooth monotone travelling wave solution exists for (1.1) if the end states are close and satisfy the Rankine-Hugoniot condition. For such a travelling wave, we shall show that if the initial data are close to a travelling wave solution, the solutions to (1.1) will approach the travelling wave solution in sup norm as the time goes to infinity. For the constitutive relations, we shall discuss two cases: convex and nonconvex.
UR - http://www.scopus.com/inward/record.url?scp=0030140594&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0030140594&partnerID=8YFLogxK
U2 - 10.1006/jdeq.1996.0067
DO - 10.1006/jdeq.1996.0067
M3 - Article
AN - SCOPUS:0030140594
VL - 127
SP - 174
EP - 196
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 1
ER -