, Volume 103, Issue 2, pp 133-144

Generalized solutions to semilinear hyperbolic systems

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Abstract

In this article semilinear hyperbolic first order systems in two variables are considered, whose nonlinearity satisfies a global Lipschitz condition. It is shown that these systems admit unique global solutions in the Colombeau algebraG(ℝ2). In particular, this provides unique generalized solutions for arbitrary distributions as initial data. The solution inG(ℝ2) is shown to be consistent with the locally integrable or the distributional solutions, when they exist.