mentor 发表于 2025-3-21 18:34:45

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发展 发表于 2025-3-21 23:47:10

Computergestützte Audio- und VideotechnikThe classical method of characteristics (MC) was developed for the construction of the solution to nonlinear first order PDE:.subject to some boundary (initial) conditions specified on a hypersurface M C .Here u = . is the unknown function of n variables ...,..., ..is a scalar function (the Hamiltonian).

无可非议 发表于 2025-3-22 03:25:00

https://doi.org/10.1007/978-3-322-83853-7Nonlinear first order PDEs arise systematically in extremal problems of dynamics, i.e. in Variation Calculus, Optimal Control and Differential Games. In Variation Calculus this equation is known as the Hamilton-Jacobi equation.

留恋 发表于 2025-3-22 07:52:07

https://doi.org/10.1007/978-3-322-83073-9Consider a two-dimensional boundary value problem on the half-plane y > 0 of the ., y)-plane:

处理 发表于 2025-3-22 12:35:59

,Planung als Instrument der Führung,Consider a system of m equations with respect to m unknowns y1,…, ym:.which in vector notations looks like:.Here the variables xi,…, .. are parameters, . is the extended vector of n + m components.

BLANC 发表于 2025-3-22 12:53:07

Introduction,The classical method of characteristics (MC) was developed for the construction of the solution to nonlinear first order PDE:.subject to some boundary (initial) conditions specified on a hypersurface M C .Here u = . is the unknown function of n variables ...,..., ..is a scalar function (the Hamiltonian).

BLANC 发表于 2025-3-22 20:02:50

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Volatile-Oils 发表于 2025-3-22 21:23:33

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BATE 发表于 2025-3-23 04:14:38

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凶猛 发表于 2025-3-23 07:32:30

Computergestützte Audio- und Videotechnikood of a reference point ..u is the scalar unknown function, u: ..., and p = (P.,., ... is the vector of its gradient, p. =.u/.x., i = 1,…, n. The scalar function . will be called the Hamiltonian, .., where.is a domain in (2n + 1)-dimensional space of ..
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查看完整版本: Titlebook: Generalized Characteristics of First Order PDEs; Applications in Opti Arik Melikyan Book 1998 Springer Science+Business Media New York 1998