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

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.