@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\textasciitilde{}v alw of u;(s*) gives sonic irlforniation about the possible structure of u near rtlc I\textasciitilde{}lowuj)p oir\textasciitilde{}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\textasciitilde{}le. Conversely, if we have -u;(.r.*) < g(uo(x*))l then smooth blow\textasciitilde{}pis possil)l{\~a} l\textasciitilde{}tlw e can compute the asymptotic pattern of thc solution as in Thc\textasciitilde{}orc\textasciitilde{}4rt.\textasciitilde{}7 . The analysis in tl\textasciitilde{}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\textasciitilde{}er.criticalc ase. On thc other hand, the results of Tl\textasciitilde{}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\textasciitilde{}lca nd will not be treated lipre. ACKNOWLEDGEMENTS \textbackslash{}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..-\textbackslash{}. 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",
}