General Solution to Unidimensional Hamilton-Jacobi Equation

Maria Lewtchuk Espindola

General Solution to Unidimensional Hamilton-Jacobi Equation

Analysis of PDEs 2013-02-05 v1 Mathematical Physics math.MP

Authors: Maria Lewtchuk Espindola

Abstract

A method for finding the general solution to the partial differential equations: \ $F(u_x,u_y)=0$ ; \ $F(f(x)\:u_x,u_y)=0$ \ (or \ $F(u_x,h(y)\:u_y)=0$ ) \ is presented, founded on a Legendre like transformation and a theorem for Pfaffian differential forms. As the solution obtained depends on an arbitrary function, then it is a general solution. As an extension of the method it is obtained a general solution to PDE: \ $F(f(x)\:u_x,u_y)=G(x)$ , and then applied to unidimensional Hamilton-Jacobi equation.

Keywords

parabolic equations partial differential equations differential equations

Cite

@article{arxiv.1302.0591,
  title  = {General Solution to Unidimensional Hamilton-Jacobi Equation},
  author = {Maria Lewtchuk Espindola},
  journal= {arXiv preprint arXiv:1302.0591},
  year   = {2013}
}

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Accepted for presentation at ICIAM 2011 - 7th International Congresson Industrial and Applied Mathematics 2011 in Vancouver, BC, Canada

General Solution to Unidimensional Hamilton-Jacobi Equation

Abstract

Keywords

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