Non-homogeneous problem for the fractional wave equation with irregular coefficients and data
Analysis of PDEs
2025-03-13 v2
Abstract
In this paper, we consider the Cauchy problem for a non-homogeneous wave equation generated by the fractional Laplacian and involving different kinds of lower order terms. We allow the equation coefficients and data to be of distributional type or less regular, having in mind the Dirac delta function and its powers, and we prove that the problem is well-posed in the sense of the concept of very weak solutions. Moreover, we prove the uniqueness in an appropriate sense and the coherence of the very weak solution concept with classical theory.
Cite
@article{arxiv.2503.07912,
title = {Non-homogeneous problem for the fractional wave equation with irregular coefficients and data},
author = {Manel Bouguenna and Mohammed Elamine Sebih},
journal= {arXiv preprint arXiv:2503.07912},
year = {2025}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2311.01639