On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems |
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Authors: | Mitsuhiro T Nakao Takehiko Kinoshita Takuma Kimura |
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Affiliation: | 1. Sasebo National College of Technology, Nagasaki, 857-1193, Japan 2. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan
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Abstract: | We present numerically verified a posteriori estimates of the norms of inverse operators for linear parabolic differential equations. In case that the corresponding elliptic operator is not coercive, existing methods for a priori estimates of the inverse operators are not accurate and, usually, exponentially increase in time variable. We propose a new technique for obtaining the estimates of the inverse operator by using the finite dimensional approximation and error estimates. It enables us to obtain very sharp bounds compared with a priori estimates. We will give some numerical examples which confirm the actual effectiveness of our method. |
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