Geodesic
Investigation of stability of stationary and periodic solutions of non-linear parabolic system
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Tome 84 (1979), pp. 286-304

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The problem of stability of solutions of nonlinear parabolic initial-boundary value problems with respect to the small disturbances of a class $C^\alpha$ with any $\alpha\geq0$ is studied under appropriate (depending on $\alpha$) restrictions on the structure of non-linear terms. 
@article{ZNSL_1979_84_a19,
     author = {A. G. Khachatryan},
     title = {Investigation of stability of stationary and periodic solutions of non-linear parabolic system},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {286--304},
     publisher = {mathdoc},
     volume = {84},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a19/}
}
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A. G. Khachatryan. Investigation of stability of stationary and periodic solutions of non-linear parabolic system. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Tome 84 (1979), pp. 286-304. http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a19/