On nonlinear parabolic equations with singular lower order term

In this paper we study existence and regularity results for solution to a nonlinear and singular parabolic problem. The model is ∂ u ∂ t - div ( ( a ( x , t ) + | u | q ) ∇ u ) = f u γ in Q , u ( x , t ) = 0 on Γ , u ( x , 0 ) = u 0 ( x ) in Ω , where Ω is a bounded open subset of R N , N ≥ 2 , Q is...

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Bibliographic Details
Published in:Journal of elliptic and parabolic equations 2022-06, Vol.8 (1), p.49-75
Main Authors: El hadfi, Youssef, El ouardy, Mounim, Ifzarne, Aziz, Sbai, Abdelaaziz
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Partial Differential Equations
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Summary:In this paper we study existence and regularity results for solution to a nonlinear and singular parabolic problem. The model is ∂ u ∂ t - div ( ( a ( x , t ) + | u | q ) ∇ u ) = f u γ in Q , u ( x , t ) = 0 on Γ , u ( x , 0 ) = u 0 ( x ) in Ω , where Ω is a bounded open subset of R N , N ≥ 2 , Q is the cylinder Ω × ( 0 , T ) , T > 0 , Γ the lateral surface ∂ Ω × ( 0 , T ) , q > 0 , γ > 0 , and f is non-negative function belonging to some Lebesgue space L m ( Q ) , m ≥ 1 and u 0 ∈ L ∞ ( Ω ) such that ∀ ω ⊂ ⊂ Ω , ∃ D ω > 0 : u 0 ≥ D ω in ω .
ISSN:2296-9020
2296-9039
DOI:10.1007/s41808-021-00138-5