This article is cited in 15 papers

Cauchy problem for $\{\vec p;\vec h\}$-parabolic equations with time-dependent coefficients

V. A. Litovchenko

Chernivtsi National University named after Yuriy Fedkovych

Abstract: 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.

UDC: 517.55

Received: 08.10.2002

DOI: 10.4213/mzm2501

 English version: Mathematical Notes, 2005, 77:3, 364–379

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