2018/07/06 by Alberto Cabada, Cabada, Alberto
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.1807.02476
openalex publication_date 2018/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to the study of the one dimensional non homogeneous\nheat equation coupled to Dirichlet Boundary Conditions.\n We obtain the explicit expression of the solution of the linear equation by\nmeans of a direct integral in an unbounded domain. The main novelty of this\nexpression relies in the fact that the solution is not given as a series of\ninfinity terms. On our expression the solution is given as a sum of two\nintegrals with a finite number of terms on the kernel.\n The main novelty is that, on the contrary to the classical method, where the\nsolutions are derived by a direct application of the separation of variables\nmethod, on the basis of the spectral theory and the Fourier Series expansion,\nthe solution is obtained by means of the application of the Laplace Transform\nwith respect to the time variable. As a consequence, for any t \≥ 0 fixed,\nwe must solve an Ordinary Differential Equation on the spatial variable,\ncoupled to Dirichlet Boundary conditions. The solution of such a problem is\ngiven by the construction of the related Green's function.\n