Publication Cover
Applicable Analysis
An International Journal
Volume 76, 2000 - Issue 3-4
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Original Articles

Representations of the solutions of partial differential equations of parabolic and hyperbolic types by means of time observations

Pages 283-289 | Received 01 Mar 2000, Published online: 10 May 2007
 

Abstract

In some general situation, the solution of a partial differential equation of parabolic type satisfying some general boundary condition is represented in the form

by using eigenvalues (λn) and eigenfunctions {φn}. In this paper, it is shown the principle of telethoscope that the solution u(t,I) is determined and represented by the observatior
where r is any fixed large positive constant and E is a small set on the closure of the space domain of the differential equation Furthermore, a general corresponding version for the solutions of differential equations of hyperbolic type is derived

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