Soluciones Clásicas a la Ecuación de Calor Lineal

Abstract

In the study of partial differential equations the heat equation is one of the most important, the first contributions to a solution of this equation were made by physicist-mathematician Jean Baptiste Joseph Fourier (1768-1830). The purpose of this text is to study the properties of some solutions found in the heat equation. First we sketch how it is possible to deduce the equation in the one-dimensional case to then raise a problem of initial values and find a first solution on which to study the properties of continuity and regularity of said solution. Then the problem of initial and boundary values on n dimensions is made and a review of the properties of the solution found using the Fourier transform is made, a study is made of the existence and uniqueness of the solution found to end with an example Of the use of this solution in one dimension.