Geodesic
Stabilization of solutions of quasilinear second order parabolic equations in domains with non-compact boundaries
Sbornik. Mathematics, Tome 201 (2010) no. 9, pp. 1249-1271

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The first mixed problem with homogeneous Dirichlet boundary condition and initial function with compact support is considered for quasilinear second order parabolic equations in a cylindrical domain $D=(0,\infty)\times\Omega$. Upper bounds are obtained, which give the rate of decay of the solutions as $t\to\infty$ as a function of the geometry of the unbounded domain $\Omega\subset \mathbb R_n$, $n\geqslant 2$. Bibliography: 18 titles.
Keywords: first mixed problem, quasilinear parabolic equations, unbounded domain, stabilization of the solution, geometric characteristic. 
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     author = {R. Kh. Karimov and L. M. Kozhevnikova},
     title = {Stabilization of solutions of quasilinear second order parabolic equations in domains with non-compact boundaries},
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R. Kh. Karimov; L. M. Kozhevnikova. Stabilization of solutions of quasilinear second order parabolic equations in domains with non-compact boundaries. Sbornik. Mathematics, Tome 201 (2010) no. 9, pp. 1249-1271. http://geodesic.mathdoc.fr/item/SM_2010_201_9_a0/