Optimal conditions of non-simultaneous blow-up and uniform blow-up profiles in localized parabolic equations

DOI10.1016/j.na.2009.07.029zbMath1180.35135OpenAlexW2060018908MaRDI QIDQ1049047

Sining Zheng, Bingchen Liu, Fengjie Li

Publication date: 8 January 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.07.029

zbMATH Keywords

homogeneous Dirichlet boundary conditionssimultaneous blow-up

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Critical exponents in context of PDEs (35B33) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58) Initial-boundary value problems for second-order parabolic systems (35K51)

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Cites Work

• Unnamed Item
• The role of nonlinear diffusion in non-simultaneous blow-up
• Coexistence of simultaneous and nonsimultaneous blow-up in a semilinear parabolic system.
• Nonexistence of positive solutions to a semilinear elliptic system and blow-up estimates for a reaction-diffusion system
• Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source
• Blowup in diffusion equations: A survey
• A semilinear parabolic system in a bounded domain
• Global existence and blow-up for a nonlinear reaction-diffusion system
• Blow-up rate for a semilinear reaction diffusion system
• Blow-up properties for parabolic systems with localized nonlinear sources.
• Critical exponents and asymptotic estimates of solutions to parabolic systems with localized nonlinear sources
• Optimal condition for non-simultaneous blow-up in a reaction-diffusion system
• The role of critical exponents in blow-up theorems: The sequel
• Global existence and finite time blow up for a reaction-diffusion system
• Uniform blow-up profiles and boundary layer for a parabolic system with localized nonlinear reaction terms
• Nonsimultaneous blow-up for a quasilinear parabolic system with reaction at the boundary
• Blow-up rate estimates for semilinear parabolic systems
• Non-simultaneous blow-up in a semilinear parabolic system
• Blowup estimates for a semilinear reaction diffusion system