科研之友
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摘要
Let us deal with the positive solutions of
partial derivative u(t)/partial derivative t = k(t)Delta(alpha)u(t)+ h(t)u(1+beta)(t), u(0, x) = phi(x) >= 0, x is an element of R-d,
where Delta(alpha) is the fractional Laplacian, 0 < alpha <= 2, and beta > 0 is a constant. We prove that under certain regularity condition on phi, h and k any non-trivial positive solution blows up in finite time. In this way we answer, in particular, the question raised in [4] for the critical case.
- 出版日期2010
