Well-Posedness in M-Ultradifferentiable Spaces for Weakly Hyperbolic Cauchy Problems with Hölder Continuous Coefficients

Said Bouaziz; Khaled Benmeriem; Laid Gasmi

doi:10.5935/jetia.v12i58.3162

Authors

Said Bouaziz Laboratory of Mathematics Modeling and Applications, University of Ahmed DRAIA, 01000, Adrar, Algeria https://orcid.org/0000-0001-9676-4889 (unauthenticated)
Khaled Benmeriem Department of Mathematics, University of Mustapha Stambouli, 29000, Mascara, Algeria. https://orcid.org/0000-0001-5241-9063 (unauthenticated)
Laid Gasmi Laboratory of Mathematics Modeling and Applications, University of Ahmed DRAIA, 01000, Adrar, Algeria https://orcid.org/0000-0001-8925-0089 (unauthenticated)

DOI:

https://doi.org/10.5935/jetia.v12i58.3162

Abstract

In this article, we demonstrate the weakly hyperbolic Cauchy problem under Hölder's regularity of a coefficient depending on time in the context of M-ultradifferentiable well-posedness. We find an equivalent condition for well-posedness within the framework of Gevrey regularity, ensuring well-posedness in a class of M-ultradifferentiable functions, dependent on the associated function of the sequence M. viscoelastic materials.