On the viscous Cauchy problem and the existence of shock profiles for a -system with a discontinuous stress function

Authors:
João-Paulo Dias and Mário Figueira

Journal:
Quart. Appl. Math. **63** (2005), 335-341

MSC (2000):
Primary 35L65

DOI:
https://doi.org/10.1090/S0033-569X-05-00960-5

Published electronically:
April 11, 2005

MathSciNet review:
2150779

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we study the existence of weak solutions for the Cauchy problem and the existence of shock profiles for the system in viscoelasticity,

with , where is a smooth stress function and is the usual Heaviside function. These kinds of models are motivated by some problems in mechanics of solids. Finally we solve, in related situations, the Riemann problem for the corresponding hyperbolic system.

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Additional Information

**João-Paulo Dias**

Affiliation:
CMAF/UL, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa - Portugal

Email:
dias@ptmat.fc.ul.pt

**Mário Figueira**

Affiliation:
CMAF/UL, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa - Portugal

Email:
figueira@ptmat.fc.ul.pt

DOI:
https://doi.org/10.1090/S0033-569X-05-00960-5

Received by editor(s):
October 5, 2004

Published electronically:
April 11, 2005

Article copyright:
© Copyright 2005
Brown University