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In this paper, we study the initial-value problem for two first order systemsin non-conservative form. The first system arises in elastodynamics and belongsto the class of strictly hyperbolic, genuinely nonlinear systems. The secondsystem has repeated eigenvalues and an incomplete set of right eigenvectors.Solutions to such systems are expected to develop singular con- centrations.Existence of singular solutions to both the systems have been shown using themethod of weak asymptotics. The second system has been shown to developsingular concentrations even from Riemann-type initial data. The first systemdiffering from the second in having an extra term containing a positiveconstant k, the solution constructed for the first system have been shown toconverge to the solution of the second as k tends to 0.

Singular solutions for a 2X2 system in nonconservative form with incomplete set of eigenvectors