Geodesic
On the stability and domain of attraction of a stationary nonsmooth limit solution of a singularly perturbed parabolic equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 3, pp. 433-444

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A stationary solution to the singularly perturbed parabolic equation $-u_t+\varepsilon^2u_{xx}-f(u,x)=0$ with Neumann boundary conditions is considered. The limit of the solution as $\varepsilon\to0$ is a nonsmooth solution to the reduced equation $f(u,x)=0$ that is composed of two intersecting roots of this equation. It is proved that the stationary solution is asymptotically stable, and its global domain of attraction is found. 
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     author = {V. F. Butuzov},
     title = {On the stability and domain of attraction of a~stationary nonsmooth limit solution of a~singularly perturbed parabolic equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {433--444},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_3_a7/}
}
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V. F. Butuzov. On the stability and domain of attraction of a stationary nonsmooth limit solution of a singularly perturbed parabolic equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 3, pp. 433-444. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_3_a7/