The latest achievements in the theory of premixed flames including both the analytical theory
and the numerical simulations are reviewed. Gas dynamics of curved flames and flame …

Reaction waves, in which an energy source sustains a wave front, occur in many areas of
physics. The most important of them is a solitary wave or autowave, which is described on a …

Recent theoretical advances in premixed gas combustion are reviewed. The attention is
focused on (1) self-acceleration of outward propagating wrinkled flames sustained by the …

It is well known that the nonlinear PDE describing the dynamics of a hydrodynamically
unstable planar flame front admits exact pole solutions as equilibrium states. Such a solution …

The problem of flame propagation is studied as an example of unstable fronts that wrinkle on
many scales. The analytic tool of pole expansion in the complex plane is employed to …

Planar flames are intrinsically unstable in open domains because of thermal expansion
across the burning front, ie, the Landau-Darrieus instability. This instability leads to wrinkling …

Premixed flame propagation is a rich interface problem. Instabilities and nonlinearities lead
to the formation of cusps pointing toward the burnt gas. These cusps, which undergo …

In a previous paper (Part I) we focused our attention on pole solutions that arise in the
context of flame propagation. The nonlinear development that follows after a planar flame …

Flame propagation is used as a prototypical example of expanding fronts that wrinkle
without limit in radial geometries but reach a simple shape in channel geometry. We show …

It is well known that the partial differential equation (PDE) describing the dynamics of a
hydrodynamically unstable planar flame front admits exact pole solutions. For such …