Electron. J. Diff. Equ., Vol. 2013 (2013), No. 58, pp. 1-11.

Singular solutions for 2x2 systems in nonconservative form with incomplete set of eigenvectors

Anupam Pal Choudhury

In this article, we study the initial-value problem for two first-order systems in non-conservative 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 Riemann-type 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; delta-shock 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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