Journal Article

On uniqueness and stability for supercritical nonlinear wave and Schrödinger equations

Michael Struwe

in International Mathematics Research Notices

Volume 2006, issue Published in print January 2006 | ISSN: 1073-7928
Published online January 2006 | e-ISSN: 1687-0247 | DOI: http://dx.doi.org/10.1155/IMRN/2006/76737
On uniqueness and stability for supercritical nonlinear wave and Schrödinger equations

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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.

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Subjects: Mathematics ; Pure Mathematics

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