Geodesic
Asymptotic properties of a solution of a boundary-value problem
Matematičeskie zametki, Tome 8 (1970) no. 3, pp. 273-284 Cet article a éte moissonné depuis la source Math-Net.Ru

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The asymptotic behavior of the solution of a boundary-value problem for the equation $u_{txx}+u_x=f$ when the time tends to infinity is investigated. It is proved that the time mean of the solution tends to a stationary solution everywhere except in a boundary region at the left end of the interval. 
@article{MZM_1970_8_3_a0,
     author = {A. M. Il'in},
     title = {Asymptotic properties of a solution of a boundary-value problem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {273--284},
     year = {1970},
     volume = {8},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_3_a0/}
}
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A. M. Il'in. Asymptotic properties of a solution of a boundary-value problem. Matematičeskie zametki, Tome 8 (1970) no. 3, pp. 273-284. http://geodesic.mathdoc.fr/item/MZM_1970_8_3_a0/