Geodesic
On the Solvability of the Inverse Problem for Determining the Right-Hand Side of a Degenerate Parabolic Equation with Integral Observation
Matematičeskie zametki, Tome 98 (2015) no. 5, pp. 710-724

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Existence and uniqueness theorems and theorems on stability under perturbations of the input data for solutions of the inverse problem for a degenerate parabolic equation in the plane with integral observation are obtained. The cases of bounded and unbounded coefficients are studied. Estimates of the solution with constants explicitly written out in terms of the input data of the problem are obtained.
Keywords: degenerate parabolic equation, solvability of the inverse problem, stability of solutions, perturbation of the input data, integral observation, maximum principle. 
@article{MZM_2015_98_5_a5,
     author = {V. L. Kamynin},
     title = {On the {Solvability} of the {Inverse} {Problem} for {Determining} the {Right-Hand} {Side} of a {Degenerate} {Parabolic} {Equation} with {Integral} {Observation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {710--724},
     publisher = {mathdoc},
     volume = {98},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a5/}
}
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V. L. Kamynin. On the Solvability of the Inverse Problem for Determining the Right-Hand Side of a Degenerate Parabolic Equation with Integral Observation. Matematičeskie zametki, Tome 98 (2015) no. 5, pp. 710-724. http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a5/