Souganidis, Panagiotis E. Recent developments in the theory of front propagation and its applications. (English) Zbl 1052.35097 Bourlioux, Anne (ed.) et al., Modern methods in scientific computing and applications. Proceedings of the NATO Advanced Study Institute and Séminaire de Mathématiques Supérieures on modern methods in scientific computing and applications, Montréal, Québec, Canada, July 9–20, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0782-5/pbk). NATO Sci. Ser. II, Math. Phys. Chem. 75, 397-449 (2002). Author’s abstract: We describe a new theory for studying the geometric motion of interfaces past the first times singularities. We also show how this theory allows one to justify and study the development of such interfaces in a wide range of applications, from the asymptotics of reaction-diffusion equations and systems and hydrodynamics limits of particle systems in phase transitions to turbulent combustion.For the entire collection see [Zbl 1045.65001]. Reviewer: Nikolai V. Krasnoschok (Donetsk) Cited in 1 Document MSC: 35K57 Reaction-diffusion equations 35B25 Singular perturbations in context of PDEs 35R35 Free boundary problems for PDEs 76F99 Turbulence 76V05 Reaction effects in flows 80A25 Combustion Keywords:viscous solution; asymptotics; geometric motion of interfaces PDFBibTeX XMLCite \textit{P. E. Souganidis}, NATO Sci. Ser. II, Math. Phys. Chem. 75, 397--449 (2002; Zbl 1052.35097)