Gudinas, G. On the Cauchy problem for the Hamilton-Jacobi equation with discontinuous initial function. (Russian. English summary) Zbl 0694.35027 Differ. Uravn. Primen. 42, 9-16 (1988). Summary: The Cauchy problem for the equation \(u_ t+f(u_ x)=0\), \(x\in {\mathbb{R}}^ n\) is studied. The solvability, uniqueness and some other properties of generalized solutions are proved for a convex f and \(\lim_{| p| \to +\infty}\frac{| f'(p)|}{F(p)}=0\), \(F(p)\equiv (p\cdot f'(p))-f(p)\). Cited in 1 Review MSC: 35F25 Initial value problems for nonlinear first-order PDEs 35D05 Existence of generalized solutions of PDE (MSC2000) 70H20 Hamilton-Jacobi equations in mechanics Keywords:Hamilton-Jacobi equation; discontinuous initial data PDFBibTeX XMLCite \textit{G. Gudinas}, Differ. Uravn. Primen. 42, 9--16 (1988; Zbl 0694.35027)