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Noncomputability in models of physical phenomena. (English) Zbl 0493.35057

MSC:
35L15 Initial value problems for second-order hyperbolic equations
35L05 Wave equation
03F60 Constructive and recursive analysis
03D80 Applications of computability and recursion theory
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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References:
[1] Grzegorczyk, A. (1955). ”Computable functionals,”Fundamenta Mathematicae,42, 168–202. · Zbl 0066.26001
[2] Grzegorczyk, A. (1957). ”On the definitions of computable real continuous functions,”Fundamenta Mathematicae,44, 61–71. · Zbl 0079.24801
[3] Pour-El, M. B., and Caldwell, J. (1975). ”On a simple definition of computable function of a real variable-with applications to functions of a complex variable,”Z. Math. Logik Grundlagen Math.,21, 1–19. · Zbl 0323.02049
[4] Pour-El, M. B., and Richards, I. (1979). ”A computable ordinary differential equation which possesses no computable solution,”Ann. Math. Logic,17, 61–90. · Zbl 0424.68028
[5] Pour-El, M. B., and Richards, I. (1981). ”The wave equation with computable initial data such that its unique solution is not computable,”Advances in Mathematics,39, 215–239. · Zbl 0465.35054
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