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The Wave Equation with Computable Initial Data Whose Unique Solution Is Nowhere Computable
Author(s) -
PourEl Marian B.,
Zhong Ning
Publication year - 1997
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19970430406
Subject(s) - statement (logic) , mathematics , point (geometry) , wave equation , computable analysis , computable function , mathematical analysis , pure mathematics , discrete mathematics , geometry , political science , law
We give a rough statement of the main result. Let D be a compact subset of ℝ 3 × ℝ. The propagation u(x, y, z, t ) of a wave can be noncomputable in any neighborhood of any point of D even though the initial conditions which determine the wave propagation uniquely are computable. A precise statement of the result appears below.