Geodesic
Cauchy problem for $\{\vec p;\vec h\}$-parabolic equations with time-dependent coefficients
Matematičeskie zametki, Tome 77 (2005) no. 3, pp. 395-411 
V. A. Litovchenko. Cauchy problem for $\{\vec p;\vec h\}$-parabolic equations with time-dependent coefficients. Matematičeskie zametki, Tome 77 (2005) no. 3, pp. 395-411. http://geodesic.mathdoc.fr/item/MZM_2005_77_3_a6/
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     title = {Cauchy problem for $\{\vec p;\vec h\}$-parabolic equations with time-dependent coefficients},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_3_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We establish the existence of a unique solution continuously depending on the initial data to the Cauchy problem for $\{\vec p;\vec h\}$-parabolic equations with time-dependent coefficients for which the initial data are generalized functions (distributions) of slow growth. For a particular class of equations, we state necessary and sufficient conditions for the existence of a unique solution of the Cauchy problem with properties of its spatial variable which are characteristic of its fundamental solution.

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