The asymptotic behavior for gaseous ignition models
The author analyzes the blow-up behavior for the classical solutions of the equation \[ u_t=\Delta u +e^u =g(t). \] Here the main difficulty arises from the nonlocal term \(g(t)\) which depends on the integral of \(u_t\) over the domain. This interesting paper includes the evolution of the blow-up singularity. It extends the result of the article by \textit{S. Bricher} [Proc. R. Soc. Edinb., Sect. A 124, No. 5, 947-969 (1994; Zbl 0818.35041)].
scientific article; zbMATH DE number 1326412