Geodesic
Families of stable manifolds for one-dimensional parabolic equations
Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 11-23

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We prove that to any invariant subset of the dynamical system generated by a one-dimensional quasilinear parabolic equation there corresponds an invariant family of stable manifolds of finite codimension. 
@article{MZM_1996_60_1_a1,
     author = {D. A. Kamaev},
     title = {Families of stable manifolds for one-dimensional parabolic equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {11--23},
     publisher = {mathdoc},
     volume = {60},
     number = {1},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a1/}
}
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D. A. Kamaev. Families of stable manifolds for one-dimensional parabolic equations. Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 11-23. http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a1/