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Young Measure Solutions of Some Nonlinear Mixed Type Equations

In: Hyperbolic Problems: Theory, Numerics, Applications

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  • H.-P. Gittel

    (University of Leipzig, Department of Mathematics)

Abstract

This contribution deals with measure-valued solutions to two types of nonlinear partial differential equations for which general existence results fail to exist. They are the potential equation for transonic flow and the associated unsteady problem (forward–backward diffusion equation). The solutions are constructed by an iteration scheme (Katchanov method) and additional time discretization (Rothe method) in the second case. The existence is proved in the sense of spatial gradient Young measures.

Suggested Citation

  • H.-P. Gittel, 2008. "Young Measure Solutions of Some Nonlinear Mixed Type Equations," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 551-558, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_53
    DOI: 10.1007/978-3-540-75712-2_53
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