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 -
TY - JOUR
T1 - Conservation laws with time dependent discontinuous coefficients
JF - SIAM J. Math. Anal. 36 (2005) 1293-1309
Y1 - 2005
A1 - Giuseppe Maria Coclite
A1 - Nils Henrik Risebro
AB - We consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11].
PB - SISSA Library
UR - http://hdl.handle.net/1963/1666
U1 - 2452
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -