# Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

• Volume: 26, Issue: 1-2, page 89-102
• ISSN: 0205-3217

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## Abstract

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MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05In 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.

## How to cite

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Dimovski, Ivan, and Tsankov, Yulian. "Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations." Mathematica Balkanica New Series 26.1-2 (2012): 89-102. <http://eudml.org/doc/281449>.

@article{Dimovski2012,
abstract = {MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05In 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.},
author = {Dimovski, Ivan, Tsankov, Yulian},
journal = {Mathematica Balkanica New Series},
keywords = {heat equations; nonlocal boundary condition; non-classical convolutions; Duhamel principle; multiplier of convolution; multiplier fraction; partial numerical multiplier; direct operational calculus},
language = {eng},
number = {1-2},
pages = {89-102},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations},
url = {http://eudml.org/doc/281449},
volume = {26},
year = {2012},
}

TY - JOUR
AU - Dimovski, Ivan
AU - Tsankov, Yulian
TI - Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations
JO - Mathematica Balkanica New Series
PY - 2012
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 26
IS - 1-2
SP - 89
EP - 102
AB - MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05In 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.
LA - eng
KW - heat equations; nonlocal boundary condition; non-classical convolutions; Duhamel principle; multiplier of convolution; multiplier fraction; partial numerical multiplier; direct operational calculus
UR - http://eudml.org/doc/281449
ER -

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