Geodesic
An initial-boundary value problem with a~noncoercive boundary condition in domains with edges
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 206-223

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We consider an initial-boundary value problem for the second order parabolic equation in a domain with edges. We assume that on a part of the boundary an unknown function satisfies the boundary condition of the type $u_t+\vec b\cdot\nabla u=\varphi$ (where $\vec b\cdot\vec n>0$, $n$ is the external normal vector, $\varphi$ is a given function). In the case of more than one space variable the existence results of general theory of parabolic initial-boundary value problems can't be applied to problems with such a boundary condition. Unique solvability of the problem under condition is established in weighted Sobolev spaces where the weight multiplies is a certain power of a distance to the edge. Bibliography: 17 titles. 
@article{ZNSL_1994_213_a11,
     author = {E. V. Frolova},
     title = {An initial-boundary value problem with a~noncoercive boundary condition in domains with edges},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {206--223},
     publisher = {mathdoc},
     volume = {213},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a11/}
}
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E. V. Frolova. An initial-boundary value problem with a~noncoercive boundary condition in domains with edges. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 206-223. http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a11/