Geodesic
Time asymptotic behavior of the solution to a quasilinear parabolic equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 12, pp. 2235-2253 Cet article a éte moissonné depuis la source Math-Net.Ru

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The time asymptotic behavior of the solution to the Cauchy problem for a quasilinear parabolic equation is analyzed. Such problems are encountered, for example, in gas dynamics and transport flow simulation. A. M. Il'in and O. A. Oleinik's well-known results are extended to a wider class of equations in which the time derivative of the unknown function is multiplied by a fixed-sign function of the former. The results have found applications in mathematical economics. 
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     author = {A. V. Gasnikov},
     title = {Time asymptotic behavior of the solution to a~quasilinear parabolic equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2235--2253},
     year = {2006},
     volume = {46},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_12_a11/}
}
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A. V. Gasnikov. Time asymptotic behavior of the solution to a quasilinear parabolic equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 12, pp. 2235-2253. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_12_a11/