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1 results

  • 23 - Boundary and Initial Boundary Value Problems for Partial Differential Equations

  • from Part V - Boundary and Initial Boundary Value Problems
  • Abner J. Salgado, University of Tennessee, Knoxville, Steven M. Wise, University of Tennessee, Knoxville
  • Book:
    Classical Numerical Analysis
    Published online:
    29 September 2022
    Print publication:
    20 October 2022, pp 611-663

  • Summary

    This chapter is a collection of facts, ideas, and techniques regarding the analysis of boundary value, initial and initial boundary value problems for partial differential equations. We begin by deriving some of the representative equations of mathematical physics, which then give rise to the classification of linear, second order, constant coefficient partial differential equations into: elliptic, parabolic, and hyperbolic equations. For each one of these classes we then discuss the main ideas behind problem with them and the existence of solutions: both classical and weak.