scholarly journals Harnack estimates for the linear heat equation under the Ricci flow

2011 ◽  
Vol 252 (1) ◽  
pp. 245-256
Author(s):  
Xiaorui Zhu
Keyword(s):  
Heat Equation ◽  
Ricci Flow ◽  
Linear Heat Equation ◽  
Linear Heat ◽  
Harnack Estimates

Variation of the Thermal Properties During Friction Under Shock Conditions

2012 ◽  
Author(s):  
G. Peillex ◽  
P. Le Tallec ◽  
F. Dambakizi
Keyword(s):  
Heat Flux ◽  
Thermal Properties ◽  
Heat Equation ◽  
Tribological Behavior ◽  
Melt Temperature ◽  
Linear Heat Equation ◽  
Linear Heat ◽  
First Results ◽  
Thermal Properties Of Materials ◽  
Properties Of Materials

During friction under shock conditions, interface is submitted to very strong heat flux. Thus, it may reach a temperature as high as melt temperature of one of the materials constituting the contact. As a consequence, the income and outcome of heat at the interface governs the friction and the contact behavior. This article exposes a model that resolves the non-linear heat equation in the vicinity of the interface. This way, it takes into account the variations of thermal properties of materials constituting the interface. First results indicate that such variations influence the tribological behavior of the contact.

scholarly journals A quasilinear parabolic perturbation of the linear heat equation

2012 ◽  
Vol 252 (1) ◽  
pp. 323-343 ◽  
Author(s):  
Santiago Cano-Casanova ◽  
Julián López-Gómez ◽  
Kazuhiro Takimoto
Keyword(s):  
Heat Equation ◽  
Linear Heat Equation ◽  
Linear Heat ◽  
Quasilinear Parabolic
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