Premium
The Heat Equation in the Interior of an Equilateral Triangle
Author(s) -
Kalimeris K.,
Fokas A. S.
Publication year - 2010
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2009.00471.x
Subject(s) - equilateral triangle , mathematics , mathematical analysis , dirichlet distribution , integral equation , dirichlet problem , boundary value problem , boundary (topology) , dirichlet integral , fourier transform , dirichlet boundary condition , space (punctuation) , dirichlet conditions , geometry , dirichlet's principle , linguistics , philosophy
We present the solution of the classical problem of the heat equation formulated in the interior of an equilateral triangle with Dirichlet boundary conditions. This solution is expressed as an integral in the complex Fourier space, i.e., the complex k 1 and k 2 planes, involving appropriate integral transforms of the Dirichlet boundary conditions. By choosing Dirichlet data so that their integral transforms can be computed explicitly, we show that the solution is expressed in terms of an integral whose integrand decays exponentially as . Hence, it is possible to evaluate this integral numerically in an efficient and straightforward manner. Other types of boundary value problems, including the Neumman and Robin problems, can be solved similarly.