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

TitleExtension of the Duhamel principle for the heat equation with Dezin's initial condition
Publication TypeJournal Article
Year of Publication2001
AuthorsChobanov G, Dimovski I
JournalAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Volume93
Pagination73-92
Keywordscommutant, convolution algebra, divisor of zero, Duhamel principle, multiplier, operational calculus
Abstract

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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