Заглавие | Extension of the Duhamel principle for the heat equation with Dezin's initial condition |
Вид публикация | Journal Article |
Година на публикуване | 2001 |
Автори | Chobanov G, Dimovski I |
Списание | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Том | 93 |
Pagination | 73-92 |
ключови думи | commutant, 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 |
Прикачен файл | Размер |
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93-073-092.pdf | 1.29 MB |