Set-valued Solutions to the Cauchy Problem for Hyperbolic Systems of Partial Differential Inclusions

Aubin, J.-P. & Frankowska, H. (1994). Set-valued Solutions to the Cauchy Problem for Hyperbolic Systems of Partial Differential Inclusions. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-94-057

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Abstract

We prove the existence of global set-valued solutions to the Cauchy problem for partial differential equations and inclusions, with either single-valued or set-valued initial conditions. The method is based on the equivalence between this problem and problem of finding viability tubes of the associated characteristic system of ordinary differential equations or differential inclusions.

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