RT Journal Article
T1 An alternative explicit expression of the kernel of the one dimensional heat equation with Dirichlet conditions
A1 Cabada Fernández, Alberto
K1 Heat equation
K1 Dirichlet problem
K1 Green’s functions
AB This paper is devoted to the study of the one dimensional non homogeneous heat equation coupled to Dirichlet Boundary Conditions. We obtain the explicit expression of the solution of the linear equation by means of a direct integral in an unbounded domain. The main novelty of this expression relies in the fact that the solution is not given as a series of infinity terms. On our expression the solution is given as a sum of two integrals with a finite number of terms on the kernel. The main novelty is that, on the contrary to the classical method, where the solutions are derived by a direct application of the separation of variables method, on the basis of the spectral theory and the Fourier Series expansion, the solution is obtained by means of the application of the Laplace Transform with respect to the time variable. As a consequence, for any  fixed, we must solve an Ordinary Differential Equation on the spatial variable, coupled to Dirichlet Boundary conditions. The solution of such a problem is given by the construction of the related Green’s function.
PB Elsevier
SN 0893-9659
YR 2018
FD 2018-10-15
LK https://hdl.handle.net/10347/45157
UL https://hdl.handle.net/10347/45157
LA eng
NO Alberto Cabada, An alternative explicit expression of the kernel of the one dimensional heat equation with Dirichlet conditions, Applied Mathematics Letters, Volume 89, 2019, Pages 97-102, ISSN 0893-9659, https://doi.org/10.1016/j.aml.2018.10.003.
NO Partially supported by Xunta de Galicia (Spain), project EM2014/032 and AIE, Spain and FEDER , grant MTM2016-75140-P.
DS Minerva
RD 26 abr 2026