The wave equation with computable initial data such that its unique solution is not computable. Pour-El, M. B. & Richards, J. I. Advances in Math., 39:215–239, 1981.
bibtex   
@ARTICLE{PR81,
  author = {Pour-El, Marian B. and Richards, J. Ian},
  title = {The wave equation with computable initial data such that its unique
	solution is not computable},
  journal = {Advances in Math.},
  year = {1981},
  volume = {39},
  pages = {215--239},
  file = {PR81.pdf:PR81.pdf:PDF},
  keywords = {bib,cca}
}

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