Nonlinear stability of rarefaction waves for a viscoelastic material with memory

Author:
Harumi Hattori

Journal:
Trans. Amer. Math. Soc. **342** (1994), 645-669

MSC:
Primary 73F15; Secondary 35L40, 73D35, 73H10

DOI:
https://doi.org/10.1090/S0002-9947-1994-1157614-5

MathSciNet review:
1157614

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we will discuss the stability of rarefaction waves for a viscoelastic material with memory. The rarefaction waves for which the stability is tested are not themselves solutions to the integrodifferential equations (1.1) governing the viscoelastic material. They are solutions to a related equilibrium system of conservation laws given by (1.11). We shall show that if the forcing term and the past history are small and if the initial data are close to the rarefaction waves, the solutions to (1.1) will approach the rarefaction waves in sup norm as the time goes to infinity.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1157614-5

Keywords:
Hyperbolic system,
rarefaction wave,
viscoelasticity

Article copyright:
© Copyright 1994
American Mathematical Society