SOLVABILITY OF THE CAUCHY PROBLEM FOR A PARABOLIC EQUATION WITH UNBOUNDED COEFFICIENTS

摘要

We consider the Cauchy problem in the half-space for a parabolic equation with unbounded initial data and lower order coefficients. We establish the solvability of the problem in the weighted space of Holder functions such that the functions, together with their derivatives, admit exponential growth as t → ∞ oo and, near the plane t = 0, the derivatives grow not faster than a power function. Bibliography: 11 titles.