Formation of Singularities in Heat Propagation Guided by Second Sound
✍ Scribed by Messaoudi A. Salim
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 227 KB
- Volume
- 130
- Category
- Article
- ISSN
- 0022-0396
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✦ Synopsis
In the classical theory of heat propagation, the flux is usually given by Newton's laws. As a result, we get a parabolic equation: namely the heat equation (e quation de chaleur). An other approach in the modern theory, is to assume that the heat flux satisfies Cattaneo's law and instead we obtain a hyperbolic system describing the propagation of the hear. Such a phenomenon, that occurs in some materials, is called propagation guided by Second Sound.
1996 Academic Press, Inc.
is assumed to hold and consequently the system (0.4), (0.5) is hyperbolic.
Global existence and decay of classical solutions, for smooth and small initial data, have been established by Coleman et al. [2]. In their paper, the authors used a classical energy argument to prove their result. As they article no.