In this paper, we analyze the null controllability property for a degenerate parabolic equation involving memory terms with a locally distributed control. We first derive a null controllability result for a nonhomogeneous degenerate heat equation via new Carleman estimates with weighted time functions that do not blow up at (Formula presented.). Then, this result is successfully used with a classical fixed point to obtain null controllability for the initial memory system.
Allal, B., Fragnelli, G. (2021). Controllability of degenerate parabolic equation with memory. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 44(11), 9163-9190 [10.1002/mma.7342].
Controllability of degenerate parabolic equation with memory
Fragnelli, Genni
2021-01-01
Abstract
In this paper, we analyze the null controllability property for a degenerate parabolic equation involving memory terms with a locally distributed control. We first derive a null controllability result for a nonhomogeneous degenerate heat equation via new Carleman estimates with weighted time functions that do not blow up at (Formula presented.). Then, this result is successfully used with a classical fixed point to obtain null controllability for the initial memory system.
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https://hdl.handle.net/11365/1279788
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