Variable Lebesgue Spaces and Hyperbolic Systems

Part I: Introduction to the Variable Lebesgue Spaces.- Introduction and motivation.- Properties of variable Lebesgue spaces.- The Hardy-Littlewood maximal operator.- Extrapolation in variable Lebesgue spaces.- Part II: Asymptotic Behaviour of Solutions to Hyperbolic Equations and Systems.- Equations with constant coefficients.- Some interesting model cases.- Time-dependent hyperbolic systems.- Effective lower order perturbations.- Examples and counter-examples.- Related topics.​