The asymptotic behavior for gaseous ignition models. (English) Zbl 0962.35085
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 S. Bricher [Proc. R. Soc. Edinb., Sect. A 124, No. 5, 947-969 (1994; Zbl 0818.35041)].
This interesting paper includes the evolution of the blow-up singularity. It extends the result of the article by S. Bricher [Proc. R. Soc. Edinb., Sect. A 124, No. 5, 947-969 (1994; Zbl 0818.35041)].
Reviewer: H.Y.Jian (Beijing)
Keywords:
semilinear parabolic equations; evolution of the blow-up singularity; blow-up behavior; nonlocal termCitations:
Zbl 0818.35041References:
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