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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.04976 |
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Table of Contents:
- In this paper, we consider the upper and lower bounds of the lifespan of classical solutions of the Cauchy problem for the one-dimensional quasilinear wave equation $u_{tt}-c(u_x)^2u_{xx}=0$ where the derivative of $c(θ)$ tends to $0$ near the origin. In particular, our result shows that the lifespan of the solution extends algebraically depending on the smallness of the initial data. Furthermore, we also show that when $c(θ)$ is flat at the origin, the lifespan extends exponentially depending on the smallness of the initial data. Our proof is based on the method of Lax's characteristics and Riemann invariants.