TY - JOUR
AU - Santiago Ayala, Yolanda
AU - Rojas Romero, Santiago
PY - 2020/07/25
Y2 - 2024/11/14
TI - Existence and Continuous Dependence of the Solution of Non homogeneous Wave Equation in Periodic Sobolev Spaces
JF - Selecciones Matemáticas
JA - Sel.Mat.
VL - 7
IS - 01
SE -
DO - 10.17268/sel.mat.2020.01.06
UR - https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2957
SP - 52-73
AB - <p>In this article, we first prove that the initial value problem associated to the homogeneous wave equation in periodic Sobolev spaces has a global solution and the solution has continuous dependence with respect to the initial data, in [0; T], T > 0. We do this in an intuitive way using Fourier theory and in a fine version introducing families of strongly continuous operators, inspired by the works of Iorio [4] and Santiago and Rojas [7].</p><p>Also, we prove that the energy associated to the wave equation is conservative in intervals [0; T], T > 0.</p><p>As a final result, we prove that the initial value problem associated to the non homogeneous wave equation has a local solution and the solution has continuous dependence with respect to the initial data and the non homogeneous part of the problem.</p>
ER -