Geodesic
Attractors of Singularly Perturbed Parabolic Systems of First Degree of Nonroughness in a Plane Domain
Matematičeskie zametki, Tome 75 (2004) no. 5, pp. 663-669 
A. Yu. Kolesov; A. N. Kulikov; N. Kh. Rozov. Attractors of Singularly Perturbed Parabolic Systems of First Degree of Nonroughness in a Plane Domain. Matematičeskie zametki, Tome 75 (2004) no. 5, pp. 663-669. http://geodesic.mathdoc.fr/item/MZM_2004_75_5_a2/
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     author = {A. Yu. Kolesov and A. N. Kulikov and N. Kh. Rozov},
     title = {Attractors of {Singularly} {Perturbed} {Parabolic} {Systems} of {First} {Degree} of {Nonroughness} in a {Plane} {Domain}},
     journal = {Matemati\v{c}eskie zametki},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_5_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study the problem of the attractors of the boundary-value problem $$ u_t=\sqrt \varepsilon (D_0 + \sqrt \varepsilon D_1)\Delta u + (A_0 + \varepsilon A_1)u + F(u),\qquad u_x|_{x=0,x=l_1} = u_y|_{y=0,y=l_2}=0, $$ where $0\le\varepsilon\ll 1$, $u\in \mathbb{R}^N$, $N\ge 3$, $\Delta $ is the Laplace operator, and $-D_0$ is the Hurwitz matrix. For such a boundary-value problem, under certain assumptions, we establish the existence of any finite fixed number of stable cycles, provided that $\varepsilon>0$ is chosen appropriately small. In other words, it is shown that this boundary-value problem involves the buffer phenomenon.

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