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Blow up for a class of quasilinear wave equations in one space dimension

✍ Scribed by Yvan Martel

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
144 KB
Volume
23
Category
Article
ISSN
0170-4214

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✦ Synopsis

For suitable

and F, we prove that all classical solutions of the quasilinear wave equation RR !( ( V ))

V "F(), with initial data of compact support, develop singularities in "nite time. The assumptions on and F include in particular the model case

O>, for q*2, and "$1. The starting point of the proof is to write the equation under the form of a "rst order system of two equations, in which F() appears as a nonlocal term. Then, we present a new idea to control the e!ect of this perturbation term, and we conclude the proof by using well-known methods developed for 2;2 systems of conservation laws.

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