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Discontinuous solutions of a nonlinear hyperbolic equation with unilateral constraints

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Abstract

We describe firstly an unilateral problem for the homogeneous wave equation in two variables, giving existence, uniqueness and continuous dependence results, and a description of the pencil of the solutions in the cases where uniqueness fails to hold. In particular we prove the existence of super- and subsolutions. We apply then the above results to the equation ytt−yxx=F(x,t,y) with unilateral constraints whose support lies on a line in a generalized half strip in the (x,t) plane.

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  1. Istituto di Matematica della Facoltà di Ingegneria, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

    Claudio Citrini

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  1. Claudio Citrini
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Citrini, C. Discontinuous solutions of a nonlinear hyperbolic equation with unilateral constraints. Manuscripta Math 29, 323–352 (1979). https://doi.org/10.1007/BF01303634

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  • DOI: https://doi.org/10.1007/BF01303634

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