Extension of the Duhamel principle for the heat equation with Dezin’s initial condition - Chobanov, Georgi; Dimovski, Ivan (Ann. Sofia Univ. Fac. Math. and Inf., 2001)
The classical Duhamel principle for the heat equation is extended to the case when the initial condition u(x,0) = f(x) is replaced by the nonlocal A. Dezin’s condition μ u(0) - u(T) = f(x), μ eq 1. To this end three types of operational calculi are developed: 1) operational calculus for ddt with the Dezin’s functional, 2) operational calculus for d^2dx^2 in a segment [0, a] with boundary conditions u(0) = 0 and u(a) = 0, and 3) a combined operational calculus for functions u(x,t) in C(Δ), Δ=[0,a]×[0,T].