Integral representation of solutions of one parabolic equation with growing coefficients in the group of minor terms

Abstract

For a degenerate parabolic equation of the second order with constant coefficients in senior terms and with growing coefficients in minor terms, we prove the representation theorems in the form of the Poisson integrals for the solutions of the Cauchy problem and for the solutions defined in an open layer and beloning to a special weight $L_p$-spaces.