Geodesic
The classical solubility of initial-boundary-value problems in the non-linear theory of oscillations of shallow shells
Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 1027-1059

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Theorems are proved concerning solutions of the Marguerre–Vlasov system of equations without taking into consideration the inertia of lateral displacements and with fixed edge boundary conditions. These results include global (with respect to time) a priori bounds on solutions, the classical solubility and the regularity of solutions. 
@article{IM2_1996_60_5_a7,
     author = {V. I. Sedenko},
     title = {The classical solubility of initial-boundary-value problems in the non-linear theory of oscillations of shallow shells},
     journal = {Izvestiya. Mathematics },
     pages = {1027--1059},
     publisher = {mathdoc},
     volume = {60},
     number = {5},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a7/}
}
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V. I. Sedenko. The classical solubility of initial-boundary-value problems in the non-linear theory of oscillations of shallow shells. Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 1027-1059. http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a7/