Blow-up phenomena for a class of fourth-order parabolic problems

Philippin, G.

doi:10.1090/S0002-9939-2015-12446-X

Blow-up phenomena for a class of fourth-order parabolic problems
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Proc. Amer. Math. Soc. 143 (2015), 2507-2513 Request permission

Abstract:

This paper deals with some qualitative properties of solutions to a class of semilinear fourth-order parabolic problems. It is shown that under certain conditions on the data, $u(\textbf {x}, t)$ cannot exist for all time and an upper bound for $t^{\star }$ is derived where $(0,t^{\star })$ is the interval of existence of $u(\textbf {x}, t)$. Moreover we construct (under certain conditions on the data) a lower bound for $t^{\star }$ when blow-up occurs. This last result is based on some Sobolev type inequality established at the end of the paper.

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