First-order Quasilinear PDEs

Chapman & Hall/CRC eBooks 2026 Book chapter

View at publisher
Authors: Harald E. Krogstad, Mohammed Yiha Dawed, Patrick M. Tchepmo Djomegni, Julien Arino
DOI: 10.1201/9781003725206-12
Cited by: 0

Abstract

This chapter gives a short introduction of first-order partial differential equations (PDEs) with emphasis on their role in models derived from conservation principles. Designed for students with a background in calculus, the exposition balances accessibility with rigor, illustrating core analytical techniques. The discussion begins with the solutions of quasi-linear PDE along characteristics, followed by the Cauchy problem, which establishes the uniqueness of the solution. The extension to systems of quasilinear PDEs is presented.

Fields of Study & Subjects

Differential Equations and Boundary Problems Advanced Mathematical Physics Problems Computational Fluid Dynamics and Aerodynamics

Publication details

Journal / source
Chapman & Hall/CRC eBooks
Pages
226–237
Publication date
30 January 2026
Language
EN
Document type
Book chapter