Abstract
A blow-up analysis for a nonlinear divergence form of parabolic equation with time-dependent coefficients is given under nonlinear boundary flux in a bounded star-shaped region. We establish some conditions on time-dependent coefficients and nonlinearities to guarantee existence of global solution or blow-up solution at some finite time t*. Moreover, an upper bound for t* is derived. Under somewhat more restrictive conditions, a lower bound for t* can be obtained. Finally, some application examples to verify the bounds of t* are presented.
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Fang, Z.B., Wang, Y. Blow-up analysis for a semilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux. Z. Angew. Math. Phys. 66, 2525–2541 (2015). https://doi.org/10.1007/s00033-015-0537-7
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DOI: https://doi.org/10.1007/s00033-015-0537-7