Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 58, pp. 111.
Singular solutions for 2x2 systems in nonconservative form with
incomplete set of eigenvectors
Anupam Pal Choudhury
Abstract:
In this article, we study the initialvalue problem for two firstorder
systems in nonconservative form. The first system arises in elastodynamics
and belongs to the class of strictly hyperbolic, genuinely nonlinear systems.
The second system has repeated eigenvalues and an incomplete set of right
eigenvectors. Solutions to such systems are expected to develop singular
concentrations. Existence of singular solutions to both the systems have
been shown using the method of weak asymptotics. The second system has
been shown to develop singular concentrations even from Riemanntype initial
data. The first system differing from the second in having an extra term
containing a positive constant k, the solution constructed for the
first system have been shown to converge to the solution of the second as
k tends to 0.
Submitted December 7, 2012. Published February 26, 2013.
Math Subject Classifications: 35L65, 35L67.
Key Words: Hyperbolic systems of conservation laws;
deltashock wave type solution; weak asymptotic method.
An addendum was attached on July 26, 2013. It corrects some misprints. See the last page of this article.
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Anupam Pal Choudhury
TIFR Centre for Applicable Mathematics
Sharada Nagar, Chikkabommasandra, GKVK P.O.
Bangalore 560065, India
email: anupam@math.tifrbng.res.in

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