Bounds for blow-up time in nonlinear parabolic problems

DOI10.1016/j.jmaa.2007.05.022zbMath1139.35055OpenAlexW2022065256MaRDI QIDQ2473895

G. A. Philippin, Lawrence E. Payne, Philip W. Schaefer

Publication date: 5 March 2008

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.2007.05.022

zbMATH Keywords

blow-upblow-up rateblow-up setnonlinear parabolic problemsdifferential inequality techniquebounds on blow-up time

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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Cites Work

• Unnamed Item
• Lower bounds for blow-up time in parabolic problems under Dirichlet conditions
• Blow-up of solutions of nonlinear heat equations
• An estimate for the best constant in a Sobolev inequality involving three integral norms
• Existenz und Regularität von Lösungen semilinearer parabolischer Anfangs-Randwertprobleme
• Best constant in Sobolev inequality
• Blowup in diffusion equations: A survey
• The problem of blow-up in nonlinear parabolic equations
• Nonexistence of global weak solutions to some properly and improperly posed problems of mathematical physics: The method of unbounded Fourier coefficients
• The Role of Critical Exponents in Blowup Theorems
• REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NONLINEAR EVOLUTION EQUATIONS
• Explosive Instabilities in Mechanics

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