Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840938 | Nonlinear Analysis: Theory, Methods & Applications | 2012 | 9 Pages |
Abstract
We prove that under some assumptions, the Hopf-type formula u(t,x)=maxq∈Rn{〈x,q〉−σ∗(q)−∫0tH(τ,q)dτ} defines a viscosity solution of the Cauchy problem for Hamilton–Jacobi equation (H,σ)(H,σ) where the initial condition σσ is convex but the Hamiltonian H=H(t,p)H=H(t,p) is not necessarily convex in pp.
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Authors
Nguyen Hoang,