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On global discontinuous solutions of Hamilton–Jacobi equations

✍ Scribed by Gui-Qiang Chen; Bo Su

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
74 KB
Volume
334
Category
Article
ISSN
1631-073X

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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;