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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

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


Author: A. A. Arkhipova
Original publication: Algebra i Analiz, tom 30 (2018), nomer 2.
Journal: St. Petersburg Math. J. 30 (2019), 181-202
MSC (2010): Primary 35K55
DOI: https://doi.org/10.1090/spmj/1537
Published electronically: February 14, 2019
MathSciNet review: 3790731
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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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Additional Information

A. A. Arkhipova
Affiliation: St. Petersburg State University, Universitetskaya nab. 7/9, 199034 St. Petersburg, Russia
Email: arinaark@gmail.com

DOI: https://doi.org/10.1090/spmj/1537
Keywords: Parabolic systems, strong nonlinearity, global solvability
Received by editor(s): September 30, 2017
Published electronically: February 14, 2019
Additional Notes: Supported by RFBR (grant no. 18-01-00472)
Dedicated: Dedicated to the 130th anniversary of Vladimir Ivanovich Smirnov
Article copyright: © Copyright 2019 American Mathematical Society