Abstract
Consider general nonlinear first order partial differential equation (PDE):
Here x = (x 1 …, x n ) is n-dimensional vector of the space \( {\mathbb{R}^n} \), D is an open neighborhood of a reference point x* \( {\mathbb{R}^n} \) u is the scalar unknown function, u: D→ \( {\mathbb{R}^n} \) 1 , and p = (P1,…, p n ) is the vector of its gradient, pi =\( \partial \)u/\( \partial \)x i , i = 1,…, n. The scalar function F will be called the Hamiltonian, F: N→ \( {\mathbb{R}^1} \) , where \( N = D \times {\mathbb{R}^1} \times {\mathbb{R}^n} \) is a domain in (2n + 1)-dimensional space of (x, u, p) \( \in {\mathbb{R}^{2n + 1}} \)
Keywords
- Characteristic Vector
- Cauchy Problem
- Characteristic Point
- Characteristic System
- Implicit Function Theorem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 1998 Springer Science+Business Media New York
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Melikyan, A. (1998). Method of Characteristics in Smooth Problems. In: Generalized Characteristics of First Order PDEs. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1758-9_2
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DOI: https://doi.org/10.1007/978-1-4612-1758-9_2
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7268-7
Online ISBN: 978-1-4612-1758-9
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