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Variations on conservation laws for the wave equation. (English) Zbl 0957.35100

This is the lecture dedicated to the Emmy Noether’s contributions to partial differential equations which was given in Berlin at the time of the ICM in August 1988. In the report are given some examples of using Noether’s theorem for conservation laws for Tricomi-like equations, for the wave equation and also for the nonlinear wave equation of the form \(u_{tt}-\Delta u=u|u|^{p-2}\). For the last equations this theorem is well-known as the so-called “abc method”. At last the author discusses the results of D. Cristodoulou and S. Klainerman and other authors about the relation of black holes to the wave equation.

MSC:

35M10 PDEs of mixed type
35L65 Hyperbolic conservation laws
35L70 Second-order nonlinear hyperbolic equations
83C57 Black holes
Full Text: DOI

References:

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