A SOLUTION TO THE CAUCHY PROBLEM FOR PARABOLIC EQUATION WITH SINGULAR COEFFICIENTS

The Cauchy problem for the second order parabolic equation with singular coefficients with respect to t at the first order spatial derivatives, is considered. A solution to this problem is constructed in explicit form. To this purpose a weighted Holder space with positive power of t as the weight, is defined. The existence, uniqueness, and estimates of the solution are proved.. Bibliography: 9 titles.
UDC 517.95 Dedicated to the 85th jubilee of V. A. Solonnikov The paper is devoted to study the Cauchy problem for a parabolic equation with coefficients singular in t at [...]