Geodesic
Cauchy problem for $\{\vec p;\vec h\}$-parabolic equations with time-dependent coefficients
Matematičeskie zametki, Tome 77 (2005) no. 3, pp. 395-411

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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. 
@article{MZM_2005_77_3_a6,
     author = {V. A. Litovchenko},
     title = {Cauchy problem for $\{\vec p;\vec h\}$-parabolic equations with time-dependent coefficients},
     journal = {Matemati\v{c}eskie zametki},
     pages = {395--411},
     publisher = {mathdoc},
     volume = {77},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_3_a6/}
}
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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/