@article{d175f6dab4e847b091295a57b88c84ac,
title = "Blowup asymptotics for scalar conservation laws with a source",
author = "Jenssen, {Helge Kristian} and Carlo Sinestrari",
note = "Funding Information: is provided by f (11)= ti{"}'. g(u) = u27n--1w. ith 172 > 1). Then we see from Lrrnrna 4.2 that thr~v alw of u;(s*) gives sonic irlforniation about the possible structure of u near rtlc I~lowuj)p oir~t.For instance. if -u;(:rf) > g(uO(x*))l (i.c. the initial valut, is too {"}spiky{"} near T * ) then we see as in Corollary 4.3 t,hat no smooth blowup is possil~le. Conversely, if we have -u;(.r.*) < g(uo(x*))l then smooth blow~pis possil)l{\~a} l~tlw e can compute the asymptotic pattern of thc solution as in Thc~orc~4rt.~7 . The analysis in tl~isc ase is more complex I)ccause Leninia 4.3 does [lot apply and n.c have to take into account some t e r m that are negligible ill thr' sul~er.criticalc ase. On thc other hand, the results of Tl~eorerns4 .8 and 4.0 apply also to this casc. The rase when -ui(z*) = g(uo(x*))li s a bortlcrliric casc whew also types of blowup different from (I), (11), (111) are possil~lca nd will not be treated lipre. ACKNOWLEDGEMENTS \Ye t,hank A. Brcssan for the opportunity of visiting S.I.S.S.A., for suggesting this problrni and for helpfill discussions. The first author thanks t.lie Department of LIatllcrrratical Sciences, NT.{"};C; Norway. for the support during the visit at S.I.S.S..-\. The nork was partially supported by ThIR project HCL # ERBFMRXCT9G0033.",
year = "1999",
doi = "10.1080/03605309908821500",
language = "English (US)",
volume = "24",
pages = "2237--2261",
journal = "Communications in Partial Differential Equations",
issn = "0360-5302",
publisher = "Taylor and Francis Ltd.",
number = "11-12",
}