 Method of Characteristics in Smooth ProblemsArik Melikyan
Chapter 1 in Generalized Characteristics of First Order PDEs, 1998, pp 7-54 from Springer Abstract: Abstract Consider general nonlinear first order partial differential equation (PDE): 1.1 $$ F\left({x,u\left( x \right),p\left( x \right)} \right) = 0,x \in D \subset {\mathbb{R}^n}\left( {p = {{\partial u} \mathord{\left/ {\vphantom {{\partial u} {\partial x = {u_x}}}} \right. \kern-\nulldelimiterspace} {\partial x = {u_x}}}} \right) $$ 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 (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1758-9_2 Ordering information: This item can be ordered from DOI: 10.1007/978-1-4612-1758-9_2 Access Statistics for this chapter More chapters in Springer Books from Springer |
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