Extension of the Duhamel principle for the heat equation with Dezin's initial condition

ЗаглавиеExtension of the Duhamel principle for the heat equation with Dezin's initial condition
Вид публикацияJournal Article
Година на публикуване2001
АвториChobanov G, Dimovski I
СписаниеAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Том93
Pagination73-92
ключови думиcommutant, convolution algebra, divisor of zero, Duhamel principle, multiplier, operational calculus
Резюме

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 $\mu u(0) - u(T) = f(x), \mu \neq 1$. To this end three types of operational calculi are developed: 1) operational calculus for $\frac{d}{dt}$ with the Dezin's functional, 2) operational calculus for $\frac{d^2}{dx^2}$ in a segment $[0, a]$ with boundary conditions $u(0) = 0$ and $u(a) = 0$, and 3) a combined operational calculus for functions $u(x,t)\textrm{ in } C(\Delta), \Delta=[0,a]\times[0,T]$.

2000 MSC

44A40

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