Geodesic
Continuability in time of smooth solutions of strong-nonlinear nondiagonal parabolic systems
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 153-167

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A class of quasilinear parabolic systems with quadratic nonlinearities in the gradient is considered. It is assumed that the elliptic operator of a system has variational structure. In the multidimensional case, the behavior of solutions of the Cauchy-Dirichlet problem smooth on a time interval [0,T) is studied. Smooth extendibility of the solution up to t=T is proved, provided that “normilized local energies” of the solution are uniformly bounded on [0,T). For the case where [0,T) determines the maximal interval of existence of a smooth solution,the Hausdorff measure of a singular set at the moment t=T is estimated.

Classification : 35K50, 35K45, 35K60 
Arkhipova, Arina. Continuability in time of smooth solutions of strong-nonlinear nondiagonal parabolic systems. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 153-167. http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_153_0/
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     title = {Continuability in time of smooth solutions of strong-nonlinear nondiagonal parabolic systems},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {153--167},
     year = {2002},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {1},
     mrnumber = {1994805},
     zbl = {1049.35093},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_153_0/}
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