Abstract
In this chapter we discuss numerical methods for the solution of general Hamilton-Jacobi equations of the form
where H can be a function of both space and time. In three spatial dimensions, we can write
as an expanded version of equation (5.1). Convection in an externally generated velocity field (equation (3.2)) is an example of a Hamilton-Jacobi equation where H(∇φ) = 0056;↦ ·∇φ. The level set equation (equation (4.4)) is another example of a Hamilton-Jacobi equation with H(∇φ) = V n |∇φ| Here V n can depend on 0078;↦, t, or even ∇φ /|∇φ|.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Osher, S., Fedkiw, R. (2003). Hamilton-Jacobi Equations. In: Level Set Methods and Dynamic Implicit Surfaces. Applied Mathematical Sciences, vol 153. Springer, New York, NY. https://doi.org/10.1007/0-387-22746-6_5
Download citation
DOI: https://doi.org/10.1007/0-387-22746-6_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9251-4
Online ISBN: 978-0-387-22746-7
eBook Packages: Springer Book Archive