Layered Viscosity Solutions of Nonautonomous Hamilton-Jacobi Equations: Semiconvexity and Relations to Characteristics

Details Layered Viscosity Solutions of Nonautonomous Hamilton-Jacobi Equations: Semiconvexity and Relations to Characteristics Layered Viscosity Solutions of Nonautonomous Hamilton-Jacobi Equations: Semiconvexity and Relations to Characteristics

2012-04-25

arxiv.org/abs/1204.5628v1

Mathematics

Analysis of PDEs

15 pages

Scientific paper

We construct an explicit representation of viscosity solutions of the Cauchy problem for the Hamilton-Jacobi equation $(H,\sigma)$ on a given domain $\Omega= (0,T)\times \R^n.$ It is known that, if the Hamiltonian $H = H(t,p)$ is not a convex (or concave) function in $p$, or $H(\cdot, p)$ may change its sign on $(0,T)$, then the Hopf-type formula does not define a viscosity solution on $\Omega.$ Under some assumptions for $H(t,p)$ on the subdomains $(t_i, t_{i+1})\times \R^n\subset \Omega$, we are able to arrange "partial solutions" given by the Hopf-type formula to get a viscosity solution on $\Omega.$ Then we study the semiconvexity of the solution as well as its relations to characteristics.

Affiliated with

Also associated with

No associations

Rating

Layered Viscosity Solutions of Nonautonomous Hamilton-Jacobi Equations: Semiconvexity and Relations to Characteristics 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 Layered Viscosity Solutions of Nonautonomous Hamilton-Jacobi Equations: Semiconvexity and Relations to Characteristics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Layered Viscosity Solutions of Nonautonomous Hamilton-Jacobi Equations: Semiconvexity and Relations to Characteristics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-137853