Existence and uniqueness results for an initial-boundary value problem of parabolic operator-differential equations in a weight space

Abstract

In this article, through the coefficients of the second order parabolic operatordifferential 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 differential equation and the weight exponent is clearly provided. A mixed problem of a partial differential equation is introduced as an applied result of this article.