Extinction of solutions of semilinear higher order parabolic equations with degenerate absorption potential

Details Extinction of solutions of semilinear higher order parabolic equations with degenerate absorption potential Extinction of solutions of semilinear higher order parabolic equations with degenerate absorption potential

2009-03-25

arxiv.org/abs/0903.4351v1

Mathematics

Analysis of PDEs

Scientific paper

We study the first vanishing time for solutions of the Cauchy-Dirichlet problem to the semilinear $2m$-order ($m \geq 1$) parabolic equation $u_t+Lu+a(x) |u|^{q-1}u=0$, $02m$ and $\displaystyle \int_0^1 s^{-1} \text{meas} \{x \in \Omega : |a(x)| \leq s \}^\frac{2m}{N} ds < + \infty$, then the solution $u$ vanishes in a finite time. When $N=2m$, the condition becomes $\displaystyle \int_0^1 s^{-1} (\text{meas} \{x \in \Omega : |a(x)| \leq s \}) (-\ln \text{meas} \{x \in \Omega : |a(x)| \leq s \}) ds < + \infty$.

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