Partial Differential Equations

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This Wikibook is UNDER CONSTRUCTION! It will hopefully be completed in the not too distant future.

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
  2. Transport equation 100% developed
  3. Test functions 100% developed
  4. Distributions 75% developed
  5. Fundamental solutions, Green's functions and Green's kernels 25% developed
  6. Poisson's equation 25% developed
  7. Heat equation 50% developed
  8. The Fourier transform 50% developed
  9. Wave equation
  10. The Malgrange-Ehrenpreis theorem
  11. Characteristic equations
  12. Sobolev spaces 25% developed
  13. Convex things
  14. Calculus of variations 0% developed
  15. Bochner's Integral
  16. Monotone operators
  17. Answers to the exercises 0% developed
  18. Appendix I: The uniform boundedness principle for (tempered) distributions 0% developed