Geodesic
Coupling the equation for filtration flow to a first order conservation law on the boundary
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 27, Tome 233 (1996), pp. 53-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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A parabolic-elliptic equation in a domain $\Omega$ is solved coupled to a first-order (hyperbolic) equation on $\partial\Omega$. The coupling is given via a nonlinear Neumann condition or if the first-order equation is linear by a variational inequality. 
@article{ZNSL_1996_233_a3,
     author = {J. Filo and S. Luckhaus},
     title = {Coupling the equation for filtration flow to a~first order conservation law on the boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {53--54},
     year = {1996},
     volume = {233},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_233_a3/}
}
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J. Filo; S. Luckhaus. Coupling the equation for filtration flow to a first order conservation law on the boundary. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 27, Tome 233 (1996), pp. 53-54. http://geodesic.mathdoc.fr/item/ZNSL_1996_233_a3/