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In this paper, we study the asymptotic behavior of blowup time for a small diffusive parabolic equation with exponential source. We prove that the blowup time of the solution converges to that of the corresponding ODE as the small diffusive approaches zero. Moreover, we show a more accurate estimate of the blowup time. Precisely, when the initial data decay near the maximum, we obtain the lower and upper bound estimates of the blowup time with a higher-order term of the peak of initial data.

Blowup time of solutions for a small diffusive parabolic problem with exponential source