Geodesic
The Cauchy Problem for a Strongly Degenerate Quasilinear Equation
Journal of the European Mathematical Society, Tome 7 (2005) no. 3, pp. 361-393

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We prove existence and uniqueness of entropy solutions for the Cauchy problem for the quasilinear parabolic equation ut​=diva(u,Du), where a(z,ξ)=∇ξ​f(z,ξ), and f is a convex function of ξ with linear growth as ∥ξ∥→∞, satisfying other additional assumptions. In particular, this class includes a relativistic heat equation and a flux limited diffusion equation used in the theory of radiation hydrodynamics.
DOI : 10.4171/jems/32
Classification : 35-XX, 00-XX
Keywords: entropy solution, quasilinear parabolic equation, relativistic heat equation, flux limited diffusion equation, radiation hydrodynamics 
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     title = {The {Cauchy} {Problem} for a {Strongly} {Degenerate} {Quasilinear} {Equation}},
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Fuensanta Andreu; Vicent Caselles; José M. Mazón. The Cauchy Problem for a Strongly Degenerate Quasilinear Equation. Journal of the European Mathematical Society, Tome 7 (2005) no. 3, pp. 361-393. doi: 10.4171/jems/32

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