heat equations nonlocal boundary condition non-classical convolutions Duhamel principle multiplier of convolution multiplier fraction partial numerical multiplier direct operational calculus
Issue Date:
2012
Publisher:
Bulgarian Academy of Sciences - National Committee for Mathematics
Citation:
Mathematica Balkanica New Series, Vol. 26, Fasc 1-2 (2012), 89p-102p
Abstract:
In this paper a method for obtaining exact solutions of the multidimensional heat equations with nonlocal boundary value conditions in a finite space domain with time-nonlocal initial condition is developed. One half of the space conditions are local, and the other are nonlocal. Extensions of Duhamel principle are obtained. In the case when the initial value condition is a local one i.e. of the form u(x1; :::; xn; 0) = f(x1; :::; xn) the problem reduces to n one-dimensional cases. In the Duhamel representations of the solution are used multidimensional non-classical convolutions. This explicit representation may be used both for theoretical study, and for numerical calculation of the solution.
