Remarks on Hamilton-Jacobi equations with measurable time-dependent Hamiltonians

Solutions of Hamilton–Jacobi Equations a

Solutions of Hamilton–Jacobi Equations and Scalar Conservation Laws with Discontinuous Space–Time Dependence

✍ Daniel N. Ostrov 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 235 KB

We establish a unique stable solution to the Hamilton-Jacobi equation x 2 ðÀ1; 1Þ; t 2 ½0; 1Þ with Lipschitz initial condition, where Kðx; tÞ is allowed to be discontinuous in the ðx; tÞ plane along a finite number of (possibly intersecting) curves parameterized by t: We assume that for fixed k;