Blow up for a class of quasilinear wave equations in one space dimension |
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Authors: | Yvan Martel |
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Abstract: | For suitable σ and F, we prove that all classical solutions of the quasilinear wave equation , with initial data of compact support, develop singularities in finite time. The assumptions on σ and F include in particular the model case , for q ⩾ 2,and ϵ = ±1. The starting point of the proof is to write the equation under the form of a first order system of two equations, in which F(ϕ) appears as a nonlocal term. Then, we present a new idea to control the effect of this perturbation term, and we conclude the proof by using well‐known methods developed for 2 × 2 systems of conservation laws. Copyright © 2000 John Wiley & Sons, Ltd. |
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