Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On the viscous Cauchy problem and the existence of shock profiles for a $p$-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
Published electronically: April 11, 2005
MathSciNet review: 2150779
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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,

\begin{displaymath}\begin{cases} \displaystyle v_t - u_x = 0, \\ \displaystyle ... ...},\quad \mu > 0, \end{cases}\quad x\in {\bf R},\,\, t \geq 0, \end{displaymath}

with $\sigma^*(v) = \sigma (v) + H(v)$, where $\sigma$ is a smooth stress function and $H$ 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: http://dx.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


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