Some Nonlinear Parabolic Problems with Singular Natural Growth Term

In this paper, we study the existence and regularity results for nonlinear parabolic problems with singular natural growth gradient terms ∂ u ∂ t - Δ p u + b ( x , t ) | ∇ u | p u θ = f in Q , u ( x , t ) = 0 on Γ , u ( x , 0 ) = 0 in Ω , where Ω is a bounded open subset of R N , N ≥ 2 , Q is the cy...

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Bibliographic Details
Published in:Resultate der Mathematik 2022-06, Vol.77 (3), Article 95
Main Authors: El Ouardy, Mounim, El Hadfi, Youssef
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:In this paper, we study the existence and regularity results for nonlinear parabolic problems with singular natural growth gradient terms ∂ u ∂ t - Δ p u + b ( x , t ) | ∇ u | p u θ = f in Q , u ( x , t ) = 0 on Γ , u ( x , 0 ) = 0 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 ) , Δ p is the so-called p - Laplace operator, Δ p u = div ( | ∇ u | p - 2 ∇ u ) with 2 ≤ p < N , b is a positive measurable bounded function, 0 < θ < 1 , and f belongs to Lebesgue space L m ( Q ) , m ≥ 1 .
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-022-01631-6