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11 December 2005 Regularization method for parabolic equation with variable operator
Valentina Burmistrova
J. Appl. Math. 2005(4): 383-392 (11 December 2005). DOI: 10.1155/JAM.2005.383


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(Ω) and Ω is a bounded domain in n with a smooth boundary Ω. L is the unbounded, nonnegative operator in L2(Ω) corresponding to a selfadjoint, elliptic boundary value problem in Ω with zero Dirichlet data on Ω. 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.


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Valentina Burmistrova. "Regularization method for parabolic equation with variable operator." J. Appl. Math. 2005 (4) 383 - 392, 11 December 2005.


Published: 11 December 2005
First available in Project Euclid: 22 December 2005

zbMATH: 1092.35037
MathSciNet: MR2204921
Digital Object Identifier: 10.1155/JAM.2005.383

Rights: Copyright © 2005 Hindawi

Vol.2005 • No. 4 • 11 December 2005
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