Total versus single point blow-up of solutions of a semilinear parabolic equation with localized reaction

DOI10.1016/S0022-247X(03)00133-1zbMath1032.35040MaRDI QIDQ1399337

Atsuko Okada, Isamu Fukuda

Publication date: 30 July 2003

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

blow-up rateblow-up setnonlocal source term

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

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Uniform blow-up rate for diffusion equations with nonlocal nonlinear source ⋮ Uniform blow-up rate for parabolic equations with a weighted nonlocal nonlinear source ⋮ Asymptotic analysis for a localized nonlinear diffusion equation ⋮ Uniform blow-up rate for a porous medium equation with a weighted localized source ⋮ Blow-up properties for a degenerate parabolic system with nonlinear localized sources ⋮ Blow-up profile for a degenerate parabolic equation with a weighted localized term ⋮ Asymptotic analysis to a parabolic equation with a weighted localized source ⋮ BLOW-UP SOLUTIONS OF THE TWO-DIMENSIONAL HEAT EQUATION DUE TO A LOCALIZED MOVING SOURCE ⋮ Infinite Fujita exponents for nonlinear diffusion equations with localized sources ⋮ Blow up behavior for a semilinear parabolic equation with localized source ⋮ Uniform blow-up rate for diffusion equations with localized nonlinear source ⋮ Total versus single point blow-up in a localized heat system ⋮ Critical exponents for non-simultaneous blow-up in a localized parabolic system ⋮ Uniform blow-up profiles for nonlinear and nonlocal reaction-diffusion equations ⋮ Blow-up behavior for a nonlinear heat equation with a localized source in a ball

Cites Work

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• Single point blow-up for a semilinear initial value problem
• Total blow-up versus single point blow-up
• The blowup property of solutions to some diffusion equations with localized nonlinear reactions
• Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source
• Total versus single point blow-up for a nonlocal gaseous ignition model
• Blow-up in Nonlocal Reaction-Diffusion Equations

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