Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 58, pp. 1-11.
Title: Singular solutions for 2x2 systems in nonconservative form with
incomplete set of eigenvectors
Author: Anupam Pal Choudhury (TIFR, Bangalore, India)
Abstract:
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.