Abstract:
The solvability of boundary value problems for fourth-order parabolic equations with changing time direction in Holder spaces is established, related to the application of the theory of singular integral equations, as well as systems of these equations. It is shown that the Ho¨lder classes of solutions to the Gevrey-type problem in the case of weighted gluing functions depend both on the non-integer Holder exponent and on the weight coefficients of the gluing conditions. Singular integral operators in Ho¨lder spaces with piecewise continuous matrix coefficients are considered. In contrast to the classical case, these operators, in addition to the singular Cauchy operator, may contain non-compact integral operators with a kernel homogeneous of degree −1 with respect to the distances to the end points of the integration contour.
Keywords:solvability, boundary value problem, parabolic equation with changing time direction, gluing condition, system of singular equations, Ho¨lder space
First page:
PDF файл