| Abstract: |
| In this talk, we discuss a diffusion model of Kirchhoff-type driven by a nonlocal integro-differential operator. Under some appropriate conditions, the local existence of nonnegative solutions is obtained by employing the Galerkin method. Then, by virtue of a differential inequality technique, we prove that the local nonnegative solutions blow-up in finite time with arbitrary negative initial energy and suitable initial values. Moreover, we give an estimate for the lower and upper bounds of the blow-up time. The main novelty is that the Kirchhoff term could be zero at the origin. |
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