%0 Journal Article
%J J. Hyperbolic Differ. Equ. 4 (2007) 771-795
%D 2007
%T Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients
%A Giuseppe Maria Coclite
%A Nils Henrik Risebro
%X 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.
%B J. Hyperbolic Differ. Equ. 4 (2007) 771-795
%I World Scientific
%G en_US
%U http://hdl.handle.net/1963/2907
%1 1793
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T10:55:33Z\\nNo. of bitstreams: 1\\nmath.AP0303288.pdf: 286583 bytes, checksum: ec274415af1f87dc1406bdc76cab8159 (MD5)
%R 10.1142/S0219891607001355
%0 Journal Article
%J SIAM J. Math. Anal. 36 (2005) 1293-1309
%D 2005
%T Conservation laws with time dependent discontinuous coefficients
%A Giuseppe Maria Coclite
%A Nils Henrik Risebro
%X 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].
%B SIAM J. Math. Anal. 36 (2005) 1293-1309
%I SISSA Library
%G en
%U http://hdl.handle.net/1963/1666
%1 2452
%2 Mathematics
%3 Functional Analysis and Applications
%$ Made available in DSpace on 2004-09-01T13:06:09Z (GMT). No. of bitstreams: 1\\n96_02.pdf: 3363466 bytes, checksum: 5ed39a522bb68737585e74668afafc5a (MD5)\\n Previous issue date: 2002
%R 10.1137/S0036141002420005