On the Fredholm Solvability for a Class of Multidimensional Hyperbolic Problems

TL;DR

This paper establishes the Fredholm alternative for a specific class of two-dimensional hyperbolic systems with mixed boundary conditions, using a regularization approach involving a right parametrix.

Contribution

It introduces a novel proof of Fredholm solvability for multidimensional hyperbolic problems with mixed boundary conditions employing regularization techniques.

Findings

Fredholm alternative proven for the class of systems

Boundary conditions include periodic and Dirichlet types

Method involves regularization via a right parametrix

Abstract

We prove the Fredholm alternative for a class of two-dimensional first-order hyperbolic systems with periodic-Dirichlet boundary conditions. Our approach is based on a regularization via a right parametrix.