What type of study is this?

This is a Quantitative Study study.

September 28, 2025Open Access

Non-homogeneous problem for the fractional wave equation with irregular coefficients and data

Key Points

The study demonstrates well-posedness for a non-homogeneous wave equation involving fractional Laplacian.
The research establishes the uniqueness of solutions within the weak solutions framework, ensuring coherence with classical methods.
It addresses the challenges posed by distributional coefficients, including Dirac delta functions and irregular data types.
The findings contribute to the mathematical understanding of wave equations, highlighting their application in advanced physical scenarios.

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.

Non-homogeneous problem for the fractional wave equation with irregular coefficients and data

Key Points

Abstract

Cite This Study