JournalsjemsVol. 7, No. 3pp. 361–393

The Cauchy Problem for a Strongly Degenerate Quasilinear Equation

  • Vicent Caselles

    Universitat Pompeu-Fabra, Barcelona, Spain
  • Fuensanta Andreu

    Universitat de Valencia, Burjassot (Valencia), Spain
  • José M. Mazón

    Universitat de Valencia, Burjassot (Valencia), Spain
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Abstract

We prove existence and uniqueness of entropy solutions for the Cauchy problem for the quasilinear parabolic equation ut=÷\a(u,Du)u_t = \div \, \a(u,Du), where \a(z,ξ)=ξf(z,ξ)\a(z,\xi) = \nabla_\xi f(z,\xi), and ff is a convex function of ξ\xi with linear growth as ξ\Vert \xi\Vert \to\infty, 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.

Cite this article

Vicent Caselles, Fuensanta Andreu, José M. Mazón, The Cauchy Problem for a Strongly Degenerate Quasilinear Equation. J. Eur. Math. Soc. 7 (2005), no. 3, pp. 361–393

DOI 10.4171/JEMS/32