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- Title
REGULARIZATION METHOD FOR PARABOLIC EQUATION WITH VARIABLE OPERATOR.
- Authors
BURMISTROVA, VALENTINA
- Abstract
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 ℝn with a smooth boundary ∂Ω. L is the unbounded, nonnegative operator in L²(Ω) corresponding to a selfadjoint, elliptic boundary value problem in . 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.
- Subjects
BOUNDARY value problems; EQUATIONS; MATHEMATICAL functions; DIRICHLET problem; OPERATOR equations
- Publication
Journal of Applied Mathematics, 2009, p383
- ISSN
1110-757X
- Publication type
Article
- DOI
10.1155/JAM.2005.383