Partial Differential Equations

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Some partial differential equations describe important processes in nature. This wikibook shows how to solve different kinds of partial differential equations and/or gives existence and uniqueness results, using a variety of methods.

Authors should be aware of the stylistic guidelines.

Table of Contents[edit]

  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