Regularization method for parabolic equation with variable operator
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, ellipt...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/JAM.2005.383 |
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| Summary: | 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 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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| ISSN: | 1110-757X 1687-0042 |