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%3MOST RECENT CS REPORTS - JANUARY 1979

@Listed below are abstracts of the most recent reports published by the Computer
Science Department of Stanford University.

@TO REQUEST REPORTS:##Check the appropriate places on the enclosed order form,
and return the entire order form page (including mailing label) by
January 12, 1979.
In many cases we can print only a limited number of copies, and requests will
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INFORMATION SERVICE, 5285 Port Royal Road, Springfield, Virginia 22161.  Stanford
Ph.D. theses are available from UNIVERSITY MICROFILMS, 300 North Zeeb Road,
Ann Arbor, Michigan 48106.
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%3STAN-CS-79-691  THE CONSTRUCTION OF INITIAL DATA FOR HYPERBOLIC SYSTEMS FROM NONSTANDARD DATA
%3Author:%1  Kenneth P. Bube↔(Thesis)
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@%3Abstract:%1@We study the first order systems of hyperbolic partial differential
equations with periodic boundary conditions in the space variables for which
complete initial data are not available.  We suppose that we can measure
%2u%1↑I , the first %2j%1 components of a solution %2u%1 of the system, perhaps
with its time derivatives, but cannot measure %2u%2∩[II] , the rest of the
components of %2u%1 , completely and accurately at any time level.  Such problems
arise in geophysical application where satelites are used to collect data.
We consider two questions.  How much information do we need to determine the
solution %2u%1 uniquely in a way which depends continuously on the data?  How
do we use these data compuationally to obtain complete initial data at some
time level?

@We investigate several approaches to answering these questions.  We show that
under certain hypotheses %2u%1∩[II] at the initial time is determined uniquely
by and depends continuously on the data obtained by measuring either %2u%1↑I over
a whole time interval or %2u%1↑I and its first time derivative at the initial
time, together ith either %2u%1∩[II] on a hyperplane in space of one lower
dimension or a finite number of Fourier coefficients of %2u%1∩[II] at
the initial time.  Our results demonstrate that it is possible to reduce the
data requirements of %2u%1∩[II] if sufficient information about %2u%2↑I is
available.

@One appliction we examine is the effect of the Coriolis term in the linearized
shallow water equations on the possibility of recovering the wind fields from
the geopotential height.

@We present algorithms and computational results for these approaches for a model
two-by-two system, and examine the method for intermittent updating currently
being used in numerical weather prediction as a method for the assimilation of
data.  Our results suggest that the use of different frequencies of updating
is important to avoid slow convergence.
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No. of pages:  119
Available in microfiche only.
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