BLOW-UP SOLUTIONS OF THE TWO-DIMENSIONAL HEAT EQUATION DUE TO A LOCALIZED MOVING SOURCE

DOI10.1142/S0219530505000443zbMath1086.35006MaRDI QIDQ4668087

W. Edward Olmstead, Colleen M. Kirk

Publication date: 18 April 2005

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

zbMATH Keywords

blow-uplaser beamreactive-diffusive mediumcombustible material

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Combustion (80A25) Volterra integral equations (45D05)

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Cites Work

• The blowup property of solutions to some diffusion equations with localized nonlinear reactions
• Analysis of explosion for nonlinear Volterra equations
• Volterra equations which model explosion in a diffusive medium
• Total versus single point blow-up of solutions of a semilinear parabolic equation with localized reaction
• General solutions for stationary/moving plane heat source problems in manufacturing and tribology
• Blow-up in a reactive-diffusive medium with a moving heat source
• The role of critical exponents in blow-up theorems: The sequel
• The influence of two moving heat sources on blow-up in a reactive-diffusive medium
• The Role of Critical Exponents in Blowup Theorems
• A diffusion equation with localized chemical reactions
• Single-point blow-up for a degenerate parabolic problem due to a concentrated nonlinear source

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