We consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal locations. 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 from [K. H. Karlsen, N. H. Risebro, and J. D. Towers, Skr. K. Nor. Vidensk. Selsk., 3 (2003), pp. 1–49], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [S. N. Kruˇzkov, Math. USSR-Sb., 10 (1970), pp. 217–243] and also partially those from Karlsen, Risebro, and Towers.
Conservation Laws with Time Dependent Discontinuous Coefficients / Coclite, Giuseppe Maria; Risebro, N. H.. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 36:4(2005), pp. 1293-1309. [10.1137/S0036141002420005]
Conservation Laws with Time Dependent Discontinuous Coefficients
COCLITE, Giuseppe Maria;
2005-01-01
Abstract
We consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal locations. 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 from [K. H. Karlsen, N. H. Risebro, and J. D. Towers, Skr. K. Nor. Vidensk. Selsk., 3 (2003), pp. 1–49], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [S. N. Kruˇzkov, Math. USSR-Sb., 10 (1970), pp. 217–243] and also partially those from Karlsen, Risebro, and Towers.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
