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Article Dans Une Revue Rendiconti del Circolo Matematico di Palermo Année : 2022

Monotone continuous dependence of solutions of singular quenching parabolic problems

Résumé

Abstract We prove the continuous dependence, with respect to the initial datum of solutions of the “quenching parabolic problem” $$\partial _{t}u-\Delta u+\chi _{\{u>0\}}u^{-\beta }=\lambda u^{p}$$ ∂ t u - Δ u + χ { u > 0 } u - β = λ u p , with zero Dirichlet boundary conditions, when $$\beta \in (0,1),p\in (0,1],\lambda \ge 0$$ β ∈ ( 0 , 1 ) , p ∈ ( 0 , 1 ] , λ ≥ 0 and $$\chi _{\{u>0\}}$$ χ { u > 0 } denotes the characteristic function of the set of points ( x , t ) where $$u(x,t)>0$$ u ( x , t ) > 0 . Notice that the absorption term $$\chi _{\{u>0\}}u^{-\beta }$$ χ { u > 0 } u - β is singular and monotone decreasing which does not allow the application of standard monotonicity arguments.

Dates et versions

hal-03762378 , version 1 (27-08-2022)

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Jesus Ildefonso Díaz, Jacques Giacomoni. Monotone continuous dependence of solutions of singular quenching parabolic problems. Rendiconti del Circolo Matematico di Palermo, 2022, ⟨10.1007/s12215-022-00814-y⟩. ⟨hal-03762378⟩
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