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

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 $\left[0,T\right)$ 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 $\left[0,T\right)$. For the case where $\left[0,T\right)$ 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
@article{ASNSP_2002_5_1_1_153_0,
author = {Arkhipova, Arina},
title = {Continuability in time of smooth solutions of strong-nonlinear nondiagonal parabolic systems},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 1},
number = {1},
year = {2002},
pages = {153-167},
zbl = {1049.35093},
mrnumber = {1994805},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2002_5_1_1_153_0}
}

Arkhipova, Arina. Continuability in time of smooth solutions of strong-nonlinear nondiagonal parabolic systems. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 1, pp. 153-167. http://www.numdam.org/item/ASNSP_2002_5_1_1_153_0/

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