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We consider a model Venttsel type problem for linear parabolic systems ofequations. The Venttsel type boundary condition is fixed on the flat part ofthe lateral surface of a given cylinder. It is defined by parabolic operator(with respect to the tangential derivatives) and the conormal derivative. TheH\"{o}lder continuity of a weak solution of the problem is proved under optimalassumptions on the data. In particular, only boundedness in the time variableof the principal matrices of the system and the boundary operator is assumed.All results are obtained by so-called A(t)-caloric method.

Regularity of weak solutions to the model Venttsel problem for solutions  of linear parabolic systems with nonsmooth in time principal matrix.  $A(t)$-caloric method