Existencia, Unicidad y Regularidad de las Soluciones a la Ecuación de Onda a través del Teorema de Hille-Yosida

Abstract

Differential equations have been a topic of discussion that emerged in the eighteenth century As a question to the behavior of the string of a violin and how to model this Phenomenon mathematically. Some related questions were being studied From the times of Pythagoras from the arhones that the rope generated according to its Length and arrangement of music in front of another set of strings. They were great mathematicians Such as Euler, D'Alembert and Daniel Bernoulli who addressed this problem, For the time, generated great questions by the methods of solution presented. This time the existence, uniqueness and regularity of the wave equation Supported in the spaces of Sobolev and the theorem of Hille-Yosida.