Geodesic
Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation
Mathematics and Education in Mathematics, Tome 41 (2012) no. 1, pp. 163-172.

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It is proposed an operational method for obtaining of explicit solutions of space-nonlocal BVPs for the two-dimensional heat equation. It is based on a direct three-dimensional operational calculus built on a three-dimensional convolution, combining the classical Duhamel convolution with two non-classical convolutions for the operators ∂xx and ∂yy. The corresponding operational calculus uses multiplier fractions instead of convolution fractions. Extensions of the Duhamel principle to the space variables are given. *2000 Mathematics Subject Classification: 44A35, 35L20, 35J05, 35J25.
Keywords: Convolution, Convolution Algebra, Multiplier, Multiplier Fractions, Heat Equation, Non-Local BVP, Duhamel Principle, Weak Solution 
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Dimovski, Ivan; Tsankov, Yulian. Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation. Mathematics and Education in Mathematics, Tome 41 (2012) no. 1, pp. 163-172. http://geodesic.mathdoc.fr/item/MEM_2012_41_1_a14/