Periodic modes of the phenomenological spin combustion equation (Q2352628)

The purpose of this paper is to study the running wave solution of a certain periodic boundary value problem. The main theorem (which is actually three different statements) states that: {\parindent=6mm \begin{itemize} \item[-] The boundary value problem has a 2-parameter family of periodic solutions. \item [-] These solutions satisfy certain relations. \item [-] The corresponding invariant torus is exponentially orbitally stable with an asymptotic phase. \end{itemize}} The proof uses a linearization around the origin, the Poincaré method of small parameters, bifurcation analysis, and spectral analysis. In the end, a global attractor for the boundary value problem is considered.