Phase Transitions and Aspects of Heat Propagation in Low Temperature Solids

Saxton, Katarzyna; Saxton, Ralph

doi:10.1142/9789812702067_0199

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2011

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“…where ε is the internal energy, ε (ϑ) = c V (ϑ), q represents heat flux, q = −α(ϑ)p, and for small |ϑ − ϑ λ |, c V satisfies a condition such as ( [12])…”

Section: Introductionmentioning

confidence: 99%

On the influence of damping in hyperbolic equations with parabolic degeneracy

Saxton

2011

Quart. Appl. Math.

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This paper examines the effect of damping on a nonstrictly hyperbolic 2×2 system. It is shown that the growth of singularities is not restricted as in the strictly hyperbolic case where dissipation can be strong enough to preserve the smoothness of solutions globally in time. Here, irrespective of the stabilizing properties of damping, solutions are found to break down in finite time on a line where two eigenvalues coincide in state space.

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“…where ε is the internal energy, ε (ϑ) = c V (ϑ), q represents heat flux, q = −α(ϑ)p, and for small |ϑ − ϑ λ |, c V satisfies a condition such as ( [12])…”

Section: Introductionmentioning

confidence: 99%

On the influence of damping in hyperbolic equations with parabolic degeneracy

Saxton

2011

Quart. Appl. Math.

Self Cite

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show abstract

Phase Transitions and Aspects of Heat Propagation in Low Temperature Solids

Cited by 1 publication

References 0 publications

On the influence of damping in hyperbolic equations with parabolic degeneracy

On the influence of damping in hyperbolic equations with parabolic degeneracy

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