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A diffusion equation in transparent media |
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| Authors: | F Andreu V Caselles J M Mazón J S Moll |
| Institution: | (1) Dept. de Análisis Matemático, Universitat de Valencia, Valencia, Spain;(2) Dept. de Tecnologia, Universitat Pompeu-Fabra, Barcelona, Spain |
| Abstract: | In this paper we study the homogeneous relativistic heat equation (HRHE) obtained as asymptotic limit of the so-called relativistic heat equation (RHE) when the kinematic viscosity ν → ∞. These equations were introduced in the theory of radiation hydrodynamics to guarantee a bounded speed of propagation of radiating energy. We shall prove that this is indeed true, and we shall construct some explicit solutions of the HRHE exhibiting fronts propagating at light speed. |
| Keywords: | Nonlinear parabolic equation linear growth functionals accretive operator nonlinear semigroups relativistic heat equation radiation hydrodynamics Monge-Kantorovich’ s mass transport theory |
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