Thomas Strömberg

Perpetual propagation of singularities for evolutionary Hamilton–Jacobi equations

Abstract This paper studies viscosity solutions S ( t , x ) of the Hamilton–Jacobi equation $$ \partial S/\partial t+H(x,\nabla S)=0,\qquad (t,x)\in (0,\infty )\times {\mathbb {R}}^n. $$ ∂ S / ∂ t + H ( x , ∇ S ) = 0 , ( t , x ) ∈ ( 0 , ∞ ) × R n . The singular set $$\Sigma (S)$$...