# American Institute of Mathematical Sciences

June  2013, 6(3): 711-722. doi: 10.3934/dcdss.2013.6.711

## Convergence to a stationary state of solutions to inverse problems of parabolic type

 1 Dipartimento di Matematica, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy

Received  April 2010 Revised  October 2010 Published  December 2012

We illustrate some results of existence and uniqueness of solutions to inverse parabolic problems of partial recostruction of the forcing term. In particular, we look for conditions assuring that the solution and the unknown part of the forcing term converge to a stationary state.
Citation: Davide Guidetti. Convergence to a stationary state of solutions to inverse problems of parabolic type. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 711-722. doi: 10.3934/dcdss.2013.6.711
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##### References:
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