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

Author(s): João-Paulo Dias; Mário Figueira
Journal: Quart. Appl. Math. 63 (2005), 335-341.
MSC (2000): Primary 35L65
Posted: April 11, 2005
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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

PII: S0033-569X-05-00960-5
Received by editor(s): October 5, 2004
Posted: April 11, 2005
Copyright of article: Copyright 2005, Brown University


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