# 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} }

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…

## 17 Citations

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