Extinction in a finite time for solutions of a class of quasilinear parabolic equations

We study the property of extinction in a finite time for nonnegative solutions of 1 q ∂ ∂ t ( u q ) - Δ ( | Δ u | p - 2 Δ u ) + a ( x ) u λ = 0 for the Dirichlet Boundary Conditions when q > λ > 0, p > 1 + q, p > 2, a ( x ) > 0 and ω a bounded domain of R N ( N > 1). We prove some necessary and sufficient conditions. The threshold is for power functions when p > 1 + q while finite time extinction occurs for very flat potentials a ( x ) when p = 1 + q. © 2022 - IOS Press. All rights reserved.