Geodesic
On the collapses of the solutions of parabolic and hyperbolic equations, possessing nonlinearities in the boundary conditions
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 15, Tome 127 (1983), pp. 75-83

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It is shown that the solutions of linear and quasi-linear equations of parabolic and hyperbolic types may destroy, provided the boundary conditions are non-linear. 
@article{ZNSL_1983_127_a4,
     author = {V. K. Kalantarov},
     title = {On the collapses of the solutions of parabolic and hyperbolic equations, possessing nonlinearities in the boundary conditions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {75--83},
     publisher = {mathdoc},
     volume = {127},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_127_a4/}
}
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V. K. Kalantarov. On the collapses of the solutions of parabolic and hyperbolic equations, possessing nonlinearities in the boundary conditions. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 15, Tome 127 (1983), pp. 75-83. http://geodesic.mathdoc.fr/item/ZNSL_1983_127_a4/