Critical exponents and asymptotic estimates of solutions to parabolic systems with localized nonlinear sources

DOI10.1016/j.jmaa.2003.12.011zbMath1052.35034OpenAlexW2088429730MaRDI QIDQ1827145

Lizhong Zhao, Sining Zheng

Publication date: 6 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2003.12.011

zbMATH Keywords

parabolic systemsblow-upcritical exponentsboundary layersglobal solutionsasymptotic estimatesblow-up ratessources of power and exponential types

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33)

Related Items (18)

The profile and boundary layer for parabolic system with critical simultaneous blow-up exponent ⋮ Blow-up solutions for localized reaction-diffusion equations with variable exponents ⋮ Life span of solutions with large initial data for a class of coupled parabolic systems ⋮ Uniform blow-up rate for parabolic equations with a weighted nonlocal nonlinear source ⋮ Blow-up for a degenerate reaction-diffusion system with nonlinear localized sources ⋮ Asymptotic analysis to a parabolic system with weighted localized sources and inner absorptions ⋮ Non-simultaneous blow-up and blow-up rates for reaction-diffusion equations ⋮ Profiles of blow-up solution of a weighted diffusion system ⋮ Non-simultaneous blow-up profile and boundary layer estimate in nonlinear parabolic problems ⋮ Uniform blow-up profiles and boundary layer for a parabolic system with nonlocal sources ⋮ Roles of weight functions in a nonlinear nonlocal parabolic system ⋮ A degenerate parabolic system with localized sources and nonlocal boundary condition ⋮ Non-simultaneous blow-up in parabolic equations coupled via localized sources ⋮ Neumann problem for reaction-diffusion systems with nonlocal nonlinear sources ⋮ Critical exponents for non-simultaneous blow-up in a localized parabolic system ⋮ Blowup properties for several diffusion systems with localised sources ⋮ Propagations of singularities in a parabolic system with coupling nonlocal sources ⋮ Optimal conditions of non-simultaneous blow-up and uniform blow-up profiles in localized parabolic equations

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• Mathematical Analysis of Thermal Runaway for Spatially Inhomogeneous Reactions
• Blow-up in Nonlocal Reaction-Diffusion Equations
• Blowup estimates for a semilinear reaction diffusion system
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