The well-posedness problem of a hyperbolic–parabolic mixed type equation on an unbounded domain

Abstract

To study the well-posedness problem of a hyperbolic–parabolic mixed type equation, the usual boundary value condition is overdetermined. Since the equation is with strong nonlinearity, the optimal partially boundary value condition can not be expressed by Fichera function. By introducing the weak characteristic function method, a different but reasonable partial boundary value condition is found first time, basing on it, the stability of the entropy solutions is established.

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Correspondence to Huashui Zhan.

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Zhan, H. The well-posedness problem of a hyperbolic–parabolic mixed type equation on an unbounded domain. Anal.Math.Phys. 9, 1849–1864 (2019). https://doi.org/10.1007/s13324-019-00280-3

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Keywords

  • Hyperbolic–parabolic mixed type equation
  • Unbounded domain
  • Optimal partially boundary value condition
  • The weak characteristic function method

Mathematics Subject Classification

  • 35L65
  • 35K85
  • 35R35