Smoothing effect and Fredholm property for first-order hyperbolic PDEs

Abstract

We give an exposition of recent results on regularity and Fredholm properties for first-order one-dimensional hyperbolic PDEs. We show that large classes of boundary operators cause an effect that smoothness increases with time. This property is the key in finding regularizers (parametrices) for hyperbolic problems. We construct regularizers for periodic problems for dissipative first-order linear hyperbolic PDEs and show that these problems are modeled by Fredholm operators of index zero.

20 pages; small corrections

References in corpus (1)

• Periodic Solutions to Dissipative Hyperbolic Systems. II: Hopf Bifurcation for Semilinear Problems

Cited by in corpus (8)

• Periodic Solutions to Dissipative Hyperbolic Systems. II: Hopf Bifurcation for Semilinear Problems
• Perturbations of superstable linear hyperbolic systems
• Classical Bounded and Almost Periodic Solutions to Quasilinear First-Order Hyperbolic Systems in a Strip
• Solution regularity and smooth dependence for abstract equations and applications to hyperbolic PDEs
• Robustness of Exponential Dichotomies of Boundary-Value Problems for General First-Order Hyperbolic Systems
• Fredholm Solvability of Time-Periodic Boundary Value Hyperbolic Problems
• On the bounded smooth solutions to exponentially stable linear nonautonomous hyperbolic systems
• Regularity of Time-Periodic Solutions to Autonomous Semilinear Hyperbolic PDEs