A case study of an Hamilton-Jacobi equation by the Adomian decompositional method

TL;DR

This paper investigates the application of the Adomian Decomposition Method to Hamilton-Jacobi equations, analyzing its efficiency and limitations in solving these equations over specific time intervals.

Contribution

It provides a case study demonstrating the effectiveness and limitations of ADM for Hamilton-Jacobi equations, including the critical time interval for solutions.

Findings

ADM yields efficient solutions only within a finite time interval

The study compares ADM with characteristic methods for solution existence

Critical time T* determines the solution's validity period

Abstract

We present a study of the Adomian's Decomposition Method (ADM) applied to the Hamilton-Jacobi equations ut + H (ux) = 0. We recall the well known characteristics methods in the case of this type of equations to justify the existence or not of solutions. This yields that the ADM gives efficient solutions in time only in ]0; T *[, where T * is the critical time of our equation.