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Regularization method for parabolic equation with variable operator
by
Valentina Burmistrova
104, 18 Kemine Str., Ashgabat, Turkmenistan
Consider the initial boundary value problem for the
equation ut=-L(t)u, u(1)=w on an interval [0, 1] for t > 0
where w(x) is a given function in L2(W), and W is a
bounded domain in Rn with a smooth boundary
¶W. L is the unbounded, nonnegative operator in
L2(W) corresponding to a selfadjoint, elliptic boundary
value problem in W with zero Dirichlet data on
¶W. The coefficients of L are assumed to be smooth
and dependent of time.
It is well known that this problem is
ill-posed in the sense that the solution does not depend
continuously on the data. We impose a bound on the solution at t=0
and at the same time allow for some imprecision in the data. Thus we
are led to the constrained problem.
There is built an approximation
solution, found error estimate for the applied method, given
preliminary error estimates for the approximate method.
Date received: June 28, 2005
Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqt-21.