Parabolic Boundary Value Problems in a Piecewise Homogeneous Wedge-Shaped Cylindrical-Circular Space with a Cavity

Parabolic Boundary Value Problems in Unlimited Piecewise Homogeneous Wedge-Shaped Hollow Cylinder

“…At the same time, for a rather wide class of linear boundary value problems in piecewise homogeneous environments, the method of hybrid integral transforms generated by the corresponding hybrid differential operators on each component of connectivity of piecewise homogeneous environment wiht different differential operators, or differential operators of the same type, but with different sets of coefficients proved to be an effective method of constructing their solutions [3,[9][10][11][12].…”

“…The main part. Let's assume that the solutions of parabolic initialboundary problems of conjugation (1)-( 4), ( 5), ( 9); (1)-( 4), ( 6), ( 9); (1)-( 4), ( 7), ( 9); (1)-( 4), ( 8), ( 9) exist, and defined and the unknown functions satisfy the conditions of applicability of direct and inverse integral and hybrid integral transforms [12,20,21].…”

“…The integral operator , m ik F due to the formula (10) as a result of identity (12) three-dimensional initial boundary value problems of conjugation (1)-( 4), ( 5), ( 9); (1)-( 4), ( 6), ( 9); (1)-( 4), ( 7), ( 9); (1)-( 4), ( 8), ( 9) puts in accordance the task of constructing classical solution of twodimensional differential equations of parabolic type of the 2nd order which is limited in the set…”

“…To the one-dimensional initial-boundary problem of conjugation ( 21)-(24) let's apply finite hybrid integral Hankel transform of 2nd kind relative to the radial variable r in piecewise homogeneous segment n I  of n conjugation points [12]:…”

“…Functions (38) define the only solutions of parabolic initial boundary problems of conjugation ( 1)-( 4), ( 5), ( 9); ( 1)-( 4), ( 6), ( 9); ( 1)-( 4), ( 7), ( 9); (1)-( 4), ( 8), ( 9) with appropriate values of ik (11,12,21,22). In formulas (38) there are components , ,,…”