Geodesic
The Cauchy problem for a nonlinear degenerate parabolic system in non-divergence form
Matematičeskie zametki SVFU, Tome 27 (2020) no. 3, pp. 27-38 Cet article a éte moissonné depuis la source Math-Net.Ru

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We deal with degenerate quasilinear parabolic systems in the non-divergence form under positive initial conditions. An asymptotic behavior of self-similar solutions in the case of slow diffusion is established. Depending on values of the numerical parameters and the initial value, the existence of the global solutions of the Cauchy problem is proved. In addition, the asymptotic representation of the solution is obtained.
Keywords: a nonlinear degenerate parabolic system, Cauchy problem.
Mots-clés : non-divergence form 
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     author = {M. Aripov and A. S. Matyakubov and B. Kh. Imomnazarov},
     title = {The {Cauchy} problem for a nonlinear degenerate parabolic system in non-divergence form},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {27--38},
     year = {2020},
     volume = {27},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2020_27_3_a2/}
}
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M. Aripov; A. S. Matyakubov; B. Kh. Imomnazarov. The Cauchy problem for a nonlinear degenerate parabolic system in non-divergence form. Matematičeskie zametki SVFU, Tome 27 (2020) no. 3, pp. 27-38. http://geodesic.mathdoc.fr/item/SVFU_2020_27_3_a2/