The Relationship between Two Approaches to a Generalized Solution of the Hamilton–Jacobi Equation
✍ Scribed by I. V. Rublev
- Book ID
- 110395139
- Publisher
- Springer
- Year
- 2002
- Tongue
- English
- Weight
- 164 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0012-2661
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📜 SIMILAR VOLUMES
The Canchy problem for a first-order partial differential equation whose left-hand side is a homogeneous function of the vector of derivatives, with the time derivative occurring additively, is considered. The boundary conditions are specified at the fight end of the time interval. The solution of a
It is proved that the function deÿned by the inÿmum-based Lax formula (for viscosity solutions) provides a solution almost everywhere in x for each ÿxed t ¿ 0 to the Hamilton-Jacobi, Cauchy problem ut + 1 2 ∇u 2 = 0; u(x; 0 + ) = v(x); where the Cauchy data function v is lower semicontinuous on rea