Complete quenching for singular parabolic problems

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Abstract

We prove finite time extinction of the solution of the equation utΔu+χ{u>0}(uβλf(u))=0 in Ω×(0,) with boundary data u(x,t)=0 on Ω×(0,) and initial condition u(x,0)=u0(x) in Ω, where ΩRN is a bounded smooth domain, 0<β<1 and λ>0 is a parameter. For every small enough λ>0 there exists a time t0>0 such that the solution is identically equal to zero.

Keywords

Parabolic equation
Quenching
Free boundary

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