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A Boundary Value Problem for a Class of Anisotropic Degenerate Parabolic–Hyperbolic Equations

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Abstract

We consider a mixed type boundary value problem for a class of degenerate parabolic–hyperbolic equations. Namely, we consider a Cartesian product domain and split its boundary into two parts. In one of them we impose a Dirichlet boundary condition; in the other, we impose a Neumann condition. We apply a normal trace formula for L 2-divergence-measure fields to prove a new strong trace property in the part of the boundary where the Neumann condition is imposed. We prove the existence and uniqueness of the entropy solution.

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Authors and Affiliations

  1. Instituto de Matemática Pura e Aplicada - IMPA, Estrada Dona Castorina, 110, Rio de Janeiro, RJ, 22460-320, Brazil

    Hermano Frid

  2. School of Mathematical Sciences, MOE-LSC, and SHL-MAC, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Yachun Li

Authors
  1. Hermano Frid
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  2. Yachun Li
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Correspondence to Hermano Frid.

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Communicated by Constantine Dafermos

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Frid, H., Li, Y. A Boundary Value Problem for a Class of Anisotropic Degenerate Parabolic–Hyperbolic Equations. Arch Rational Mech Anal 226, 975–1008 (2017). https://doi.org/10.1007/s00205-017-1148-6

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  • DOI: https://doi.org/10.1007/s00205-017-1148-6

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