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The wave equation with computable initial data such that its unique solution is not computable. (English) Zbl 0465.35054

##### MSC:
 35L05 Wave equation 03F60 Constructive and recursive analysis
##### Keywords:
noncomputable real number; computable function
Full Text:
##### References:
 [1] Grzegorczyk, A, Computable functionals, Fund. math., 42, 168-202, (1955) · Zbl 0066.26001 [2] Grzegorczyk, A, On the definitions of computable real continuous functions, Fund. math., 44, 61-71, (1957) · Zbl 0079.24801 [3] Hellwig, G, Partial differential equations, (1964), Blaisdell New York · Zbl 0133.35701 [4] Kreisel, G, A notion of mechanistic theory, Synthese, 29, 11-16, (1974) · Zbl 0307.02028 [5] Mostowski, A, On computable sequences, Fund. math., 44, 37-51, (1957) · Zbl 0079.24702 [6] Myhill, J, A recursive function defined on a compact interval and having a continuous derivative that is not recursive, Michigan math. J., 18, 97-98, (1971) · Zbl 0218.02029 [7] Petrovskii, I.G, Partial differential equations, (1967), Saunders Philadelphia · Zbl 0139.03403 [8] Pour-El, M.B; Caldwell, J, On a simple definitions of computable function of a real variable—with applications to functions of a complex variable, Z. math. logik. grundlagen math., 21, 1-19, (1975) · Zbl 0323.02049 [9] Pour-El, M.B; Richards, I, A computable ordinary differential equation which possesses no computable solution, Ann. of math. logic, 17, 61-90, (1979) · Zbl 0424.68028
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