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

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dc.creatorBelaud, Yves
dc.creatorShishkov, Andrey
dc.date2009-03-25
dc.date.accessioned2026-07-07T12:56:29Z
dc.date.available2026-07-07T12:56:29Z
dc.descriptionWe study the first vanishing time for solutions of the Cauchy-Dirichlet problem to the semilinear $2m$-order ($m \geq 1$) parabolic equation $u_t+Lu+a(x) |u|^{q-1}u=0$, $0<q<1$ with $a(x) \geq 0$ bounded in the bounded domain $Ω\subset \R^N$. We prove that if $N>2m$ and $\displaystyle \int_0^1 s^{-1} \text{meas} \{x \in Ω: |a(x)| \leq s \}^\frac{2m}{N} ds < + \infty$, then the solution $u$ vanishes in a finite time. When $N=2m$, the condition becomes $\displaystyle \int_0^1 s^{-1} (\text{meas} \{x \in Ω: |a(x)| \leq s \}) (-\ln \text{meas} \{x \in Ω: |a(x)| \leq s \}) ds < + \infty$.
dc.identifierhttps://arxiv.org/abs/0903.4351
dc.identifierhttp://arxiv.org/abs/0903.4351
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224600
dc.subjectAnalysis of PDEs
dc.subject35B40, 35K20, 35P15
dc.titleExtinction of solutions of semilinear higher order parabolic equations with degenerate absorption potential
dc.typetext

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