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Abstract
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We consider the system
,
where
is a real number
and the unknowns
and
belong to convenient spaces of distributions. For this simplified model from
elastodynamics, a rigorous solution concept defined in the setting of a distributional
product is used. The explicit solution of a Riemann problem and the possible emergence
of a
shock wave are established. For initial conditions containing a Dirac measure, a
shock
wave solution is also presented.
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Keywords
products of distributions, nonconservative systems,
nonstrictly hyperbolic systems, strictly hyperbolic
systems, $\delta$ waves, $\delta^\prime$ waves, Riemann
problem.
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Mathematical Subject Classification 2010
Primary: 35D99, 35L67, 46F10
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Milestones
Received: 1 March 2017
Accepted: 26 October 2017
Published: 5 January 2018
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