Geodesic
Singularly perturbed two-dimensional parabolic problem in the case of intersecting roots of the reduced equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 4, pp. 646-654

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The singularly perturbed parabolic equation $-u_t+\varepsilon^2\Delta u-f(u,x,\varepsilon)=0$, $x\in D\subset\mathbb R^2$, $t>0$ with Robin conditions on the boundary of $D$ is considered. The asymptotic stability as $t\to\infty$ and the global domain of attraction are analyzed for the stationary solution whose limit as $\varepsilon\to0$ is a nonsmooth solution to the reduced equation $f(u,x,0)=0$ that consists of two intersecting roots of this equation. 
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     author = {V. F. Butuzov},
     title = {Singularly perturbed two-dimensional parabolic problem in the case of intersecting roots of the reduced equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {646--654},
     publisher = {mathdoc},
     volume = {47},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_4_a6/}
}
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V. F. Butuzov. Singularly perturbed two-dimensional parabolic problem in the case of intersecting roots of the reduced equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 4, pp. 646-654. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_4_a6/