1. Partial Differential Equations

  1. Pavel Šolín

Published Online: 30 NOV 2005

DOI: 10.1002/0471764108.ch1

Partial Differential Equations and the Finite Element Method

Partial Differential Equations and the Finite Element Method

How to Cite

Šolín, P. (2005) Partial Differential Equations, in Partial Differential Equations and the Finite Element Method, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471764108.ch1

Publication History

  1. Published Online: 30 NOV 2005
  2. Published Print: 4 NOV 2005

ISBN Information

Print ISBN: 9780471720706

Online ISBN: 9780471764106

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Summary

Chapter 1 features an introduction to the theory of partial differential equations (PDEs). Assumed is the knowledge of the elementary functional analysis provided in Appendix A. Discussed is the classification of PDEs, the notion of well-posedness, and selected general existence and uniqueness results for operator equations. The most frequently used types of PDEs — the second-order elliptic, parabolic and hyperbolic equations, are discussed in detail. Covered are their weak formulations, various types of boundary conditions, existence and uniqueness results, maximum principles and various other properties and results. Discussed are linear first-order hyperbolic systems and their solution via the characteristic lines, the Riemann problem, and the creation of discontinuities (shock waves) in nonlinear hyperbolic PDEs.