Beyond partial differential equations: A course on linear and quasi-linear abstract hyperbolic evolution equations

TL;DR

This paper/course introduces semigroup methods for solving linear and quasi-linear hyperbolic PDEs, emphasizing applications in relativistic physics and wave equations, showcasing their potential in current research.

Contribution

It presents a comprehensive course on semigroup techniques applied to hyperbolic evolution equations, including nonlinear cases and physical applications.

Findings

Semigroup methods effectively solve hyperbolic PDEs.

Applications demonstrate relevance to relativistic physics.

Potential for advancing research in hyperbolic systems.

Abstract

This course introduces the use of semigroup methods in the solution of linear and nonlinear (quasi-linear) hyperbolic partial differential equations, with particular application to wave equations and Hermitian hyperbolic systems. Throughout the course applications to problems from current relativistic (hyperbolic) physics are provided, which display the potential of semigroup methods in the solution of current research problems in physics.