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

2009/03/25 by Belaud, Yves, Shishkov, Andrey
Mathematics · #35B40 #35K20 #35P15 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.0903.4351

openalex publication_date 2009/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the first vanishing time for solutions of the Cauchy-Dirichlet problem to the semilinear 2m-order (m ≥ 1) parabolic equation u_t+Lu+a(x) |u|^q-1u=0, 02m and ∫₀¹ s^-1 meas \x ∈ Ω: |a(x)| ≤ s \^(2m)/(N) ds < + ∞, then the solution u vanishes in a finite time. When N=2m, the condition becomes ∫₀¹ s^-1 (meas \x ∈ Ω: |a(x)| ≤ s \) (-ln meas \x ∈ Ω: |a(x)| ≤ s \) ds < + ∞.

Citations

• Long-time extinction of solutions of some semilinear parabolic equations

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