Phragmén–Lindelöf alternative and continuous dependence-type results for the thermoelasticity of type III

Abstract

In this article, equations of thermoelasticity of type III in three-dimensional cylindrical domain are studied. We prove a Phragmén–Lindelöf alternative result, i.e. the smooth solutions either grow or decay exponentially as the distance from the entry section tends to infinity. In the decay case, the authors indicate how to bound explicitly the total energy in terms of data. The continuous dependence of the solutions on the coefficient ρ is also proved in this article.

Keywords:

• Phragmén–Lindelöf alternative
• continuous dependence
• thermoelasticity of type III
• Saint-Venant's principle
• hyperbolic equations

2000 Mathematics Subject Classifications:

• Primary 35B40
• 35L20
• 35L15

Acknowledgements

The work was supported by the national Science Foundation of China (Grant #10471050), Guangdong Province natural Science Foundation of China (Grants #031495, #7005795) and University Special Research Fund for Ph.d. Program (Grant #20060574002).