Geodesic
Verification of asymptotic solutions for one-dimensional nonlinear parabolic equations
Matematičeskie zametki, Tome 52 (1992) no. 3, pp. 10-16.

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The present article proves a result that is new for partial differential equations. According to this result, the solution of the Cauchy problem for a nonlinear parabolic equation with variable, slowly changing coefficients will turn into (asymptotically approach) a special asymptotic solution, either a solution or a kink, for high values of $t$. 
@article{MZM_1992_52_3_a1,
     author = {S. A. Vakulenko},
     title = {Verification of asymptotic solutions for one-dimensional nonlinear parabolic equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {10--16},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1992_52_3_a1/}
}
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S. A. Vakulenko. Verification of asymptotic solutions for one-dimensional nonlinear parabolic equations. Matematičeskie zametki, Tome 52 (1992) no. 3, pp. 10-16. http://geodesic.mathdoc.fr/item/MZM_1992_52_3_a1/