Heat flow for a class of quadratic functionals with nondiagonal principal matrix. Existence of a smooth global solution

Arkhipova, A.

doi:10.1090/spmj/1537

Heat flow for a class of quadratic functionals with nondiagonal principal matrix. Existence of a smooth global solution
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by A. A. Arkhipova

St. Petersburg Math. J. 30 (2019), 181-202

DOI: https://doi.org/10.1090/spmj/1537

Published electronically: February 14, 2019

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Abstract:

A class of quasilinear parabolic systems with nondiagonal principal matrices and strongly nonlinear additional terms is considered. The elliptic operator of the system has a variational structure. The existence of a global smooth solution is proved in the case of two spatial variables.

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