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Bounds on Blow-Up Time for a Higher-Order Non-Newtonian Filtration Equation

  • Bui Le Trong Thanh , Nguyen Ngoc Trong und Tan Duc Do EMAIL logo
Veröffentlicht/Copyright: 15. Juni 2023
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ABSTRACT

Let d ∈ {1, 2, 3, . . .} and Ω ⊂ ℝd be open bounded with Lipschitz boundary. Consider the reaction-diffusion parabolic problem

P { ut|x|4+Δ(|Δu|m2Δu)=k(t)|u|p1u(x,t)Ω×(0,T),u(x,t)= xju(x,t)=0,(x,t)Ω×(0,T),j{1,,d},u(x,0)=u0(x),xΩ,

where T > 0, m ∈ [2, ∞), p ∈ (1, ∞) and 0u0W02,m(Ω)Lp+1(Ω) . We investigate the upper and lower bounds on the blow-up time of a weak solution to (P).

2020 Mathematics Subject Classification: Primary 35B44; Secondary 35K25; 35K30

(Communicated by Alberto Lastra)


Funding statement: This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number T2022-18-01.

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Received: 2021-11-01
Accepted: 2022-06-27
Published Online: 2023-06-15

© 2023 Mathematical Institute Slovak Academy of Sciences

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