Geodesic
Stabilization of solutions of pseudo-differential parabolic equations in unbounded domains
Izvestiya. Mathematics , Tome 74 (2010) no. 2, pp. 325-345

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We consider the first mixed problem in a cylindrical domain $D=(0,\infty)\times\Omega$ for a pseudo-differential parabolic equation with homogeneous Dirichlet boundary conditions and a finitely supported initial function. We find upper bounds for the $L_2$-norm of a solution as $t\to\infty$ in terms of a geometric characteristic introduced earlier by the author for an unbounded domain $\Omega\subset\mathbb R^n$, $n\geqslant 2$, in the case of a higher-order parabolic equation.
Keywords: stabilization of solutions, pseudo-differential parabolic equations, unbounded domain, mixed problem. 
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     author = {L. M. Kozhevnikova},
     title = {Stabilization of solutions of pseudo-differential parabolic equations in unbounded domains},
     journal = {Izvestiya. Mathematics },
     pages = {325--345},
     publisher = {mathdoc},
     volume = {74},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2010_74_2_a3/}
}
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L. M. Kozhevnikova. Stabilization of solutions of pseudo-differential parabolic equations in unbounded domains. Izvestiya. Mathematics , Tome 74 (2010) no. 2, pp. 325-345. http://geodesic.mathdoc.fr/item/IM2_2010_74_2_a3/