Geodesic
On the Stabilization to Zero of the Solutions of the Inverse Problem for a Degenerate Parabolic Equation with Two Independent Variables
Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 860-870

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Theorems on the stabilization to zero as $t\to +\infty$ of solutions of the inverse problem of determining the unknown right-hand side of a degenerate parabolic equation with one space variable belonging to a bounded closed interval are proved under an integral observation condition. Further, it is assumed that the coefficients of the equation are unbounded. These theorems can be used to obtain an upper bound for the stabilization rate. The paper contains examples of equations for which the assumptions of the theorems hold, as well as an example showing that such assumptions are essential.
Keywords: degenerate parabolic equation, asymptotic behavior, inverse problem. 
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     author = {V. L. Kamynin},
     title = {On the {Stabilization} to {Zero} of the {Solutions} of the {Inverse} {Problem} for a {Degenerate} {Parabolic} {Equation} with {Two} {Independent} {Variables}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {860--870},
     publisher = {mathdoc},
     volume = {101},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a6/}
}
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V. L. Kamynin. On the Stabilization to Zero of the Solutions of the Inverse Problem for a Degenerate Parabolic Equation with Two Independent Variables. Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 860-870. http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a6/