TY - JOUR
T1 - Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients
JF - J. Hyperbolic Differ. Equ. 4 (2007) 771-795
Y1 - 2007
A1 - Giuseppe Maria Coclite
A1 - Nils Henrik Risebro
AB - 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.
PB - World Scientific
UR - http://hdl.handle.net/1963/2907
U1 - 1793
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -