Abstract
Abstract
We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely determine the semi-discrete source. This means the observed area can be extremely small, and that is the reason we call it sparse boundary data. For the numerical reconstruction, we formulate the problem from the Bayesian sequential prediction perspective and conduct the numerical examples which estimate the space-time-dependent source state by state. To better demonstrate the method’s performance, we solve two common multiscale problems from two models with a long source sequence. The numerical results illustrate that the inversion is accurate and efficient.
Funder
National Science Foundation
the Fundamental Research Funds for the Central Universities, Sun Yat-sen University
National Natural Science Foundation of China
U.S. Department of Energy
Brookhaven National Laboratory
Subject
Applied Mathematics,Computer Science Applications,Mathematical Physics,Signal Processing,Theoretical Computer Science
Cited by
3 articles.
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