Analysis and Mathematical Physics

, Volume 9, Issue 4, pp 1849–1864 | Cite as

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

  • Huashui ZhanEmail author


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.


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

Mathematics Subject Classification

35L65 35K85 35R35 


Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Applied MathematicsXiamen University of TechnologyXiamenChina

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