Viscosity solutions of Hamilton--Jacobi equations with discontinuous coefficients

Details Viscosity solutions of Hamilton--Jacobi equations with discontinuous coefficients Viscosity solutions of Hamilton--Jacobi equations with discontinuous coefficients

2003-03-24

arxiv.org/abs/math/0303288v1

Mathematics

Analysis of PDEs

20 pages, 1 figure

Scientific paper

We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to ``internal boundaries''. By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\infty$, and that the limits are viscosity solutions.

Affiliated with

Also associated with

No associations

Rating

Viscosity solutions of Hamilton--Jacobi equations with discontinuous coefficients does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Viscosity solutions of Hamilton--Jacobi equations with discontinuous coefficients, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Viscosity solutions of Hamilton--Jacobi equations with discontinuous coefficients will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-449127