Geodesic
On parabolic problems with non-Lipschitz nonlinearity
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), Tome 21 (2007), pp. 62-76

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We consider parabolic problems with non-Lipschitz nonlinearities in different scales of Banach spaces and prove local-in-time existence theorems. A new class of parabolic equations that have analytic solutions is obtained. 
@article{CMFD_2007_21_a2,
     author = {O. \`E. Zubelevich},
     title = {On parabolic problems with {non-Lipschitz} nonlinearity},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {62--76},
     publisher = {mathdoc},
     volume = {21},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2007_21_a2/}
}
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O. È. Zubelevich. On parabolic problems with non-Lipschitz nonlinearity. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), Tome 21 (2007), pp. 62-76. http://geodesic.mathdoc.fr/item/CMFD_2007_21_a2/