## EXISTENCE AND UNIQUENESS RESULTS FOR AN INITIAL-BOUNDARY VALUE PROBLEM OF PARABOLIC OPERATOR-DIFFERENTIAL EQUATIONS IN A WEIGHT SPACE

## EXISTENCE AND UNIQUENESS RESULTS FOR AN INITIAL-BOUNDARY VALUE PROBLEM OF PARABOLIC OPERATOR-DIFFERENTIAL EQUATIONS IN A WEIGHT SPACE

*A. B. I. Ahmed*

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## Abstract

In this article, through the coecients of the second order parabolic operator- dierential equation, the regular solvability problem with initial-boundary conditions is proved in a weight space. The association between the lower bound of the spectrum of the self-adjoint operator in the main part of the dierential equation and the weight exponent is clearly provided. A mixed problem of a partial dierential equation is intro- duced as an applied result of this article.

## Keywords

operator-dierential equation, multiple characteristics, Hilbert space, regular solvability.