Partial Differential Equations

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This wikibook aims at explaining how to solve partial differential equations, and if that's not possible, how to at least obtain some uniqueness and existence results.

Table of contents[edit]

  1. Introduction
  2. Method of characteristics
  3. Calculus of variations
  4. Fourier-analytic methods (requires Fourier analysis)
  5. The wave equation (requires integration on manifolds)
  6. Fundamental solutions (requires distribution theory)
  7. Poisson's equation (requires integration on manyfolds and harmonic function theory)
  8. The heat equation
  9. Sobolev spaces (requires some functional analysis)
  10. Monotone operators (requires convex analysis)

Old table of Contents[edit]

Authors should be aware of the stylistic guidelines.

Water drop 001.jpg
  1. Introduction and first examples 100% developed

Linear partial differential equations[edit]

  1. The transport equation 100% developed
  2. Test functions 100% developed
  3. Distributions 100% developed
  4. Fundamental solutions, Green's functions and Green's kernels 100% developed
  5. The heat equation 75% developed
  6. Poisson's equation 25% developed
  7. The Fourier transform 75% developed
  8. The wave equation 0% developed
  9. The Malgrange-Ehrenpreis theorem 50% developed

Nonlinear partial differential equations[edit]

  1. The characteristic equations 0% developed
  2. Sobolev spaces 25% developed
  3. Convex analysis 0% developed
  4. Calculus of variations 0% developed
  5. Bochner's Integral 0% developed
  6. Monotone operators 0% developed

  1. Answers to the exercises 0% developed
  2. Appendix I: The uniform boundedness principle for (tempered) distributions 0% developed