JournalsjemsVol. 7 , No. 3DOI 10.4171/jems/32

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
The Cauchy Problem for a Strongly Degenerate Quasilinear Equation cover

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.