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On uniqueness and stability for supercritical nonlinear wave and Schrödinger equations

Struwe, Michael

In: International Mathematics Research Notices, 2006, vol. 2006, p. -

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    Title
    • On uniqueness and stability for supercritical nonlinear wave and Schrödinger equations
    Author
    • Struwe, Michael. Departement Mathematik, ETH Zürich, 8092 Zürich, Switzerland
    Document Type
    • Postprint
    Classification
    • Health
    Keywords
    OAI-PMH Identifier
    • oai:doc.rero.ch:297765
    Summary
    We show that smooth solutions to nonlinear wave and Schrödinger equations involving coercive nonlinearities of polynomial type with arbitrarily strong growth are unique among distribution solutions satisfying the energy inequality. The result also yields the stability of classical solutions in the energy norm and may be used to show convergence of the approximate solutions obtained by standard approximation schemes to the true solution in this norm