# On the existence and cusp singularity of solutions to semilinear generalized Tricomi equations with discontinuous initial data

@article{Ruan2012OnTE,
title={On the existence and cusp singularity of solutions to semilinear generalized Tricomi equations with discontinuous initial data},
author={Zhuoping Ruan and Ingo Witt and Huicheng Yin},
journal={Communications in Contemporary Mathematics},
year={2012},
volume={17},
pages={1450028}
}
• Published 2 November 2012
• Mathematics
• Communications in Contemporary Mathematics
In this paper, we are concerned with the local existence and singularity structures of low regularity solution to the semilinear generalized Tricomi equation with typical discontinuous initial data (u(0, x), ∂tu(0, x)) = (0, φ(x)), where m ∈ ℕ, x = (x1,…,xn), n ≥ 2, and f(t, x, u) is C∞ smooth on its arguments. When the initial data φ(x) is homogeneous of degree zero or piecewise smooth along the hyperplane {t = x1 = 0}, it is shown that the local solution u(t, x) ∈ L∞([0, T] × ℝn) exists and…
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