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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Vasileva A. B., Butuzov V. F., Asimptoticheskie metody v teorii singulyarnykh vozmuschenii, Vyssh. shkola, M., 1990 | MR

[2] Butuzov V. F., Nefedov H. H., Shnaider K. P., “Singulyarno vozmuschennye zadachi v sluchae smeny ustoichivosti”, Differents. ur-niya. Singulyarnye vozmuscheniya, Itogi nauki i tekhn. Ser. “Sovrem. matem. i ee prilozh.” Tematicheskie obzory, 109, VINITI, M., 2002, 5–242

[3] Butuzov V. F., Nefedov N. N., Schneider K. R., “Singularly perturbed elliptic problems in the case of exchange of stabilities”, J. Different. Equat., 169 (2001), 373–395 | DOI | MR | Zbl

[4] Pao C. V., Nonlinear parabolic and elliptic equations, Plenum Press, New York, 1992 | MR