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Archive for Rational Mechanics and Analysis

, Volume 226, Issue 3, pp 975–1008 | Cite as

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

  • Hermano FridEmail author
  • Yachun Li
Article

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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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Instituto de Matemática Pura e Aplicada - IMPARio de JaneiroBrazil
  2. 2.School of Mathematical Sciences, MOE-LSC, and SHL-MACShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China

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